Basic Electronics - College Algebra Course Manual

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Electronics

Section 1.1 Electronics Safety

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afety is everyone’s responsibility. Everyone must cooperate to create the safest possible working conditions. Where your personal life and good health are concerned, safety becomes your responsibility whether you step in front of a speeding truck, or expose yourself to a lethal shock, are matters over which you, as an individual have more control than anyone else.

Safety is simply a matter of applying common sense precautions. The rules of safety are concerned with the prevention of accidental injuries sustained when an accident occurs.

The general rules for shop safety apply equally to the electrical-electronics laboratory. The following important shop rules should be observed at all times.

+ + + +

1-1 Electronics Safety

1-2 Applications of Electronics

1-3 Digital Number Systems

1-4 Representing Binary Quantities

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1. Don’t clown around or engage in horseplay. Many painful injuries are caused by the carelessness and thoughtless antics of the clown.

2. Get your teacher’s approval before starting your work. This will save your time and help prevent accidents. Remember your teacher is there to help you.

3. Report all injuries at once, even the slightest. A small cut can develop serious complications if not properly treated.

4. Wear safety glasses- when grinding or working in areas where sparks or chips of metals are flying. Remember that your eyes is a priceless possession.

5. Keep the floors around your work area clean and free of litter which might cause someone to slip or stumble.

6. Use tools correctly and do not use them if they are not in proper working condition. 7. Observe the proper methods of handling and lifting objects. Get help to lift heavy

objects.

8. Do not talk nor disturb a fellow student when he is operating a machine.

9. Never leave the machine while it is running down. Stay with it until it stops completely.

10. Obtain permission before you use power tools.

Students and teachers who work with electricity face hazard of electrical shock and should make every effort to understand the danger.

Electricity can cause fatal burns or cause vital organs to malfunction. In general, a current of 5 mA or less will cause a sensation of shock, but rarely any damage. Larger currents can cause hand muscles to contract. Currents on the order of 100 mA are often fatal if they pass through the body for even a few seconds.

The Electronics Workshop is primarily concerned with low-voltage electronics. The chance of injury due to electric shock is very, very, low. Experiments for younger students have been designed to be easily completed without the use of soldering.

Nonetheless, as in all laboratory situations, there are safety rules that must be followed. The two most important safety rules are:

1. Always have a knowledgeable adult to supervise work. Ask a teacher or parent to help you.

2. Always use common sense and pay attention to the job you are working on. Doing so can prevent most laboratory accidents.

Electricity-electronics is a tremendous field and most of us do well to understand small segments of it. Ask questions when in doubt. Be humble!

Every possible precaution has been taken to ensure the safety of experiments and the correctness of information.

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between radio frequency equipment to produce the carrier wave radiated from the antenna and the audio and video equipment in the studio that supplies the modulating signal with the desired information.

High-fidelity audio equipment can be considered with radio receivers. The receiver itself has audio amplifiers to drive the loudspeaker that reproduce the sound.

Satellite communications is also a transmit-receive system using electro-magnetic radio waves. The satellite just happens to be orbiting around the earth at a height of about 22,300 miles order to maintain a stationary position relative to the earth. Actually, the satellite is a relay station for transmitter and receiver earth stations.

Electric Power. These applications are in the generation and distribution if 60-Hz AC power, as the source of energy for electrical equipment. Included are lighting, heating, motors, and generators. Electronics plays an important role in the control and monitoring of electrical equipments.

Digital Electronics. We see the digits 0 to 9 on an electronic calculator or digital watch, but digital electronics has a much broader meaning. The circuits for digital applications operate with pulses of voltage or current, as shown in the diagram below. A pulse waveform is either completely ON or OFF because of the sudden changes in amplitude. In-between values have no function. Note that ON and OFF stage can also be labeled as HIGH and LOW, or 1 and 0 in binary notation. Effectively the digital pulses correspond to the action of switching circuits that are either on or off.

Voltage or current variations with a continuous set of values form an analog waveform, as shown below. The 60-Hz power line and audio and video signals are common examples. Note that the values between 0 and 10 V are marked to indicate that all the in-between values are an essential part of a waveform.

Actually, all the possible applications in the types of electronic circuits can be divided into two just two types- digital circuits that recognize pulses when they are HIGH or LOW, and analog circuits that use all values in the waveform. The applications of digital electronics, including calculators, computers, data processing and data communications, possibly form the largest branch of electronics. In addition many other applications, including radio and television, use both analog and digital circuits.

In addition to all the general applications in communications, digital equipment, and electric services, several fields that could be of specific interest include automotive electronics, industrial electronics, and medical electronics. Both digital and analog techniques are used.

In automotive electronics, more and more electronic equipment is used in cars for charging the battery, power assist functions, measuring gages, and monitoring and control of engine performance. Perhaps the most important application is the electronic ignition. This method provides better timing

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of the ignition spark, especially at high speeds. On-board computer monitor and control a wide auto functions.

Industrial electronics includes control of welding and heating processes, the use of elevator control, operation of copying machines. Metal detectors and smoke detectors, moisture control, and computer-controlled machinery. In addition there are many types of remote control-functions, such as automatic garage door openers and burglar alarms. Closed-circuit television is often used for surveillance.

Medical electronics combines electronics with biology. Medical research diagnosis, and treatment all use electronic equipment. Examples are the electron microscope and electrocardiograph machine. In hospitals, oscilloscopes are commonly used as the display to monitor the heartbeat of patients in extensive care.

Job titles

Different specialties in electronics are indicated by the following titles for engineers: antenna, audio, computer, digital, illumination, information theory, magnetic, microwave, motors and generators, packaging, power distribution, radio, semiconductor, television, and test equipment. Many of these fields combine physics and chemistry, especially for semiconductors.

The types of jobs in these fields include engineer for research, development, production, sales, or management, teacher, technician, technical writer, computer programmer, drafter, service worker, tester and inspector. Technicians and service workers are needed for testing, maintenance and repair of all the different types of electronic equipments.

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(2 points each) a. b. c. d. e.

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Resistors

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he resistor's function is to reduce the flow of electric current. This symbol is used to indicate a resistor in a circuit diagram, known as a schematic.

Resistance value is designated in units called the "Ohm." A 1000 Ohm resistor is typically shown as 1Ohm ( kilo Ohm ), and 1000 K-Ohms is written as 1M-Ohm ( mega ohm ).

There are two classes of resistors; fixed resistors and the variable resistors. They are also classified according to the material from which they are made. The typical resistor is made of either carbon film or metal film. There are other types as well, but these are the most common.

The resistance value of the resistor is not the only thing to consider when selecting a resistor for use in a circuit. The "tolerance" and the electric power ratings of the resistor are also important.

The tolerance of a resistor denotes how close it is to the actual rated résistance value. For example, a ±5% tolerance would indicate a resistor that is within ±5% of the specified resistance value.

The power rating indicates how much power the resistor can safely tolerate. Just like you wouldn't use a 6 volt flashlight lamp to replace a burned out light in your house, you wouldn't use a 1/8 watt resistor when you should be using a 1/2 watt resistor.

The maximum rated power of the resistor is specified in Watts. Power is calculated using the square of the current ( I2 ) x the resistance value ( R ) of the resistor. If the maximum rating of the resistor is exceeded, it will become extremely hot, and even burn. Resistors in electronic circuits are typically rated 1/8W, 1/4W, and 1/2W. 1/8W is almost always used in signal circuit applications. When powering a light emitting diode, comparatively large current flows through the resistor, so you need to consider the power rating of the resistor you choose.

C H A P T E R

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2-1 Types of Resistors

2-2 Resistor Color Codes

2-3 The Ohmmeter 2-4 The Ohmeter 2-5 The Multimeter 2-6 Variable Resistors 2 -7 Rating of Resistors 2-8 Resistor Troubles + + + +

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This is the most general purpose, cheap resistor. Usually the tolerance of the resistance value is

±5%. Power ratings of 1/8W, 1/4W and 1/2W are frequently used.

Carbon film resistors have a disadvantage; they tend to be electrically noisy. Metal film resistors are recommended for use in analog circuits. However, I have never experienced any problems with this noise.

The physical size of the different resistors are as follows.

From the top of the photograph 1/8W 1/4W 1/2W Rough size Rating power (W) Thickness (mm) Length (mm) 1/8 2 3 1/4 2 6 1/2 3 9

This resistor is called a Single-In-Line(SIL) resistor network. It is made with many resistors of the same value, all in one package. One side of each resistor is connected with one side of all the other resistors inside. One example of its use would be to control the current in a circuit powering many light emitting diodes (LEDs).

In the photograph on the left, 8 resistors are housed in the package. Each of the leads on the package is one resistor. The ninth lead on the left side is the common lead. The face value of the resistance is printed. ( It depends on the supplier. )

Some resistor networks have a "4S" printed on the top of the resistor network. The 4S indicates that the package contains 4 independent resistors that are not wired together inside. The housing has eight leads instead of nine. The internal wiring of these typical resistor networks has been illustrated below. The size (black part) of the resistor network which I have is as follows: For the type with 9 leads, the thickness is 1.8 mm, the height 5mm, and the width 23 mm. For the types with 8 component leads, the thickness is 1.8 mm, the height 5 mm, and the width 20 mm.

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Metal film resistors

Metal film resistors are used when a higher tolerance (more accurate value) is needed. They are much more accurate in value than carbon film resistors. They have about ±0.05% tolerance. They have about ±0.05% tolerance. I don't use any high tolerance resistors in my circuits. Resistors that are about ±1% are more than sufficient. Ni-Cr (Nichrome) seems to be used for the material of resistor. The metal film resistor is used for bridge circuits, filter circuits, and low-noise analog signal circuits.

From the top of the photograph 1/8W (tolerance ±1%) 1/4W (tolerance ±1%) 1W (tolerance ±5%) 2W (tolerance ±5%) Rough size Rating power (W) Thickness (mm) Length (mm) 1/8 2 3 1/4 2 6 1 3.5 12 2 5 15

CDS Elements

Some components can change resistance value by changes in the amount of light hitting them. One type is the Cadmium Sulfide Photocell. (Cd) The more light that hits it, the smaller its resistance value becomes.

There are many types of these devices. They vary according to light sensitivity, size, resistance value etc.

Pictured at the left is a typical CDS photocell. Its diameter is 8 mm, 4 mm high, with a cylinder form. When bright light is hitting it, the value is about 200 ohms, and when in the dark, the resistance value is about 2M ohms. This device is using for the head lamp illumination confirmation device of the car.

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resistor is the Ceramic resistor. These are wirewound resistors in a ceramic case, strengthened with a special cement. They have very high power ratings, from 1 or 2 watts to dozens of watts. These resistors can become extremely hot when used for high power applications, and this must be taken into account when designing the circuit. These devices can easily get hot enough to burn you if you touch one.

The photograph on the left is of wirewound resistors. The upper one is 10W and is the length of 45 mm, 13 mm thickness.

The lower one is 50W and is the length of 75 mm, 29 mm thickness.

The upper one is has metal fittings attached. These devices are insulated with a ceramic coating.

The photograph on the left is a ceramic (or cement) resistor of 5W and is the height of 9 mm, 9 mm depth, 22 mm width.

Thermistor ( Thermally sensitive resistor )

The resistance value of the thermistor changes according to temperature.

This part is used as a temperature sensor.There are mainly three types of thermistor. NTC(Negative Temperature Coefficient Thermistor)

: With this type, the resistance value decreases continuously as the temperature rises. PTC(Positive Temperature Coefficient Thermistor)

: With this type, the resistance value increases suddenly when the temperature rises above a specific point.

CTR(Critical Temperature Resister Thermistor)

: With this type, the resistance value decreases suddenly when the temperature rises above a specific point.

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The relation between the temperature and the resistance value of the NTC type can be calculated using the following formula.

R : The resistance value at the temperature T T : The temperature [K]

R0: The resistance value at the reference temperature T0

T0 : The reference temperature [K]

B : The coefficient

As the reference temperature, typically, 25°C is used.

The unit with the temperature is the absolute temperature(Value of which 0 was -273°C) in K(Kelvin). 25°C are the 298 Kelvins.

Section 2.2 Resistor color code

Because carbon resistors are small physically, they are color-coded to mark their value in ohms. The basis of this system is the use of colors for numerical values as listed in the table below. In memorizing the colors note that the darkest colors, black and brown, are for the lowest numbers, zero and one, whereas white is for nine. The color coding is standardized by the Electronic Industries Association (EIA). These colors are also used for small capacitors.

Example 1 (Brown=1),(Black=0),(Orange=3) 10 x 103 = 10k ohm Tolerance(Gold) = ±5% Example 2 (Yellow=4),(Violet=7),(Black=0),(Red=2) 470 x 102 = 47k ohm Tolerance(Brown) = ±1%

Color Value Multiplier Tolerance (%) Black 0 0 -Brown 1 1 ±1 Red 2 2 ±2 Orange 3 3 ±0.05 Yellow 4 4 -Green 5 5 ±0.5 Blue 6 6 ±0.25 Violet 7 7 ±0.1 Gray 8 8 -White 9 9 -Gold - -1 ±5 Silver - -2 ±10 None - - ±20

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insulating body, which is usually tan. Reading from left to right, the first band close to the edge gives the first digit in numerical value of R. The next band marks the second digit. The third band is the decimal multiplier, which gives the number of zeroes after the two digits.

Resistors under 10ΩΩΩΩ. For these values the third stripe is either gold or silver, indicating a fractional decimal multiplier. When the third digit is gold, multiply the first two digits by 0.1. Example, if the first two digits are 25 then, 25 X 0.1 = 2.5 Ω. Silver means a mult4iplier of 0.01 . If the first two digits is still 25 then, 25 X 0.01 = .25 Ω.

It is important to realize that the gold and silver colors are used as decimal multipliers only in the third stripe. However, gold and silver are used most often in the fourth stripe to indicate how accurate the R value is.

Resistor Tolerance. The amount by which the actual R can be different from the color-coded value is the tolerance, usually given in percent. For instance, a 2000Ω resistor with 10 percent tolerance can have resistance 10 percent above or below the coded value. This R, therefore, is between 1800Ω to 2200Ω. The calculation are as follows:

10 percent of 2000 is .1 X 2000 = 200 For + 10 percent, the value is

2000 + 200 = 2200Ω

For – 10 percent, the value is 2000 – 200 = 1800Ω

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Score: Instructor’s signature: _______ Date: Remarks:

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I. Fill up the table below for the expected value of the resistors in ohms and in kilo-ohms given its color codes below. (2 points per number)

Value in Ohms Value in K-ohms 1. Grey, Blue, Red, Silver

2. Yellow, Green, Gold, Gold 3. Violet, Brown, Black, Silver, Gold 4. Brown, Black, Red, Gold

5. Blue, Yellow, Orange, Silver 6. Brown, Black, Silver, Silver 7. Red, Red, Red, Gold

8. Green, Orange, Brown, Silver 9. Brown, Violet, Yellow, Gold 10. Blue, Black, Red, Orange, Gold

II. Compute for the tolerance value of each resistor given its color codes.(2 points per number)

1. Red, Brown, Orange, Gold a. Upper Limit b. Lower Limit

2. Orange, Violet, Brown, Silver a. Upper Limit

b. Lower Limit

3. Grey, White, Violet, Gold, Silver a. Upper Limit

b. Lower Limit 4. Blue, Green, Silver, Gold

a. Upper Limit b. Lower Limit 5. Brown, Black, Gold, Silver

a. Upper Limit b. Lower Limit

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1,000 megohms.

The ohmmeter consists of a dc ammeter, with a few added features. The added features are: A dc source of potential (usually a 3-volt battery)

One or more resistors (one of which is variable) A simple ohmmeter circuit is shown in figure 2-1. The ohmmeter's pointer deflection is controlled by the amount of battery current passing through the moving coil. Before measuring the resistance of an unknown resistor or electrical circuit, the test leads of the ohmmeter are first shorted together, as shown in figure 1-31.

With the leads shorted, the meter is calibrated for proper operation on the selected range. While the leads are shorted, meter current is maximum and the pointer deflects a maximum amount, somewhere near the zero position on the ohms scale. Because of this current through the meter with the leads shorted, it is necessary to remove the test leads when you are finished using the ohmmeter. If the leads were left connected, they could come in contact with each other and discharge the ohmmeter battery. When the variable resistor (rheostat) is adjusted properly, with the leads shorted, the pointer of the meter will come to rest exactly on the zero position. This indicates

ZZZZero Resistance

ero Resistance

Between the test leads, which, in fact, are shorted together. The zero reading of a series-type ohmmeter is on the right-hand side of the scale, where as the zero reading for an ammeter or a voltmeter is generally to the left-hand side of the scale. (There is another type of ohmmeter which is discussed a little later on in this chapter.) When the test leads of an ohmmeter are separated, the pointer of the meter will return to the left side of the scale.

The interruption of current and the spring tension act on the movable coil assembly, moving the pointer to the left side (∞) of the scale.

Figure 1-31. - A simple ohmmeter circuit.

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U

Using the Ohmmeter

sing the Ohmmeter

After the ohmmeter is adjusted for zero reading, it is ready to be connected in a circuit to measure resistance. A typical circuit and ohmmeter arrangement is shown in figure 2-2

Figure 2-2. - Measuring circuit resistance with an ohmmeter.

The power switch of the circuit to be measured should always be in the OFF position. This prevents the source voltage of the circuit from being applied across the meter, which could cause damage to the meter movement.

The test leads of the ohmmeter are connected in series with the circuit to be measured (fig. 1-32). This causes the current produced by the 3-volt battery of the meter to flow through the circuit being tested. Assume that the meter test leads are connected at points a and b of figure 1-32. The amount of current that flows through the meter coil will depend on the total resistance of resistors R1 and R2, and the resistance of

the meter. Since the meter has been preadjusted (zeroed), the amount of coil movement now depends solely on the resistance of R1and R2. The inclusion of R1 and R2 raises the

total series resistance, decreasing the current, and thus decreasing the pointer deflection. The pointer will now come to rest at a scale figure indicating the combined resistance of R1 and R2.

If R1 or R2, or both, were replaced with a resistor(s) having a larger value, the current flow in the

moving coil of the meter would be decreased further. The deflection would also be further decreased, and the scale indication would read a still higher circuit resistance.

Movement of the moving coil is proportional to the amount of current flow.

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Ohmmeter Ranges

hmmeter Ranges

The amount of circuit resistance to be measured may vary over a wide range. In some cases it may be only a few ohms, and in others it may be as great as 1,000,000 ohms (1 megohm). To enable the meter to indicate any value being measured, with the least error, scale multiplication features are used in most ohmmeters. For example, a typical meter will have four test lead jacks-COMMON, R X 1, R X 10, and R X 100. The jack marked COMMON is connected internally through the battery to one side of the moving coil of the ohmmeter. The jacks marked R X 1, R X 10, and R X 100 are connected to three different size resistors located within the ohmmeter. This is shown in figure 2-3.

Figure 1-33. - An ohmmeter with multiplication jacks.

Some ohmmeters are equipped with a selector switch for selecting the multiplication scale desired, so only two test lead jacks are necessary.

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amount to cause a useful pointer deflection. If the R X 100 range were used to measure the same 3,750-ohm resistor, the pointer would deflect still further, to the 37.5-ohm position. This increased deflection would occur because resistor R X 100 has about 1/10 the resistance of resistor R X 10. The foregoing circuit arrangement allows the same amount of current to flow through the meter's moving coil whether the meter measures 10,000 ohms on the R X 10 scale, or 100,000 ohms on the R X 100 scale.

It always takes the same amount of current to deflect the pointer to a certain position on the scale (midscale position for example), regardless of the multiplication factor being used. Since the multiplier resistors are of different values, it is necessary to ALWAYS "zero" adjust the meter for each multiplication fact or selected.

You should select the multiplication factor (range) that will result in the pointer coming to rest as near as possible to the midpoint of the scale. This enables you to read the resistance more accurately, because the scale readings are more easily interpreted at or near midpoint.

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Ohmmeter Safety Precautions

hmmeter Safety Precautions

The following safety precautions and operating procedures for ohmmeters are the MINIMUM necessary to prevent injury and damage.

Be certain the circuit is deenergized and discharged before connecting an ohmmeter. Do not apply power to a circuit while measuring resistance.

When you are finished using an ohmmeter, switch it to the OFF position if one is provided and remove the leads from the meter.

Always adjust the ohmmeter for 0 (or ∞ in shunt ohmmeter) after you change ranges before making the resistance measurement.

Section 2.4 The Multimeter

A MULTIMETER is the most common measuring device used in the Navy. The name multimeter comes from MULTIple METER, and that is exactly what a multimeter is. It is a dc ammeter, a dc voltmeter, an ac voltmeter, and an ohmmeter, all in one package. Figure 1-37 is a picture of a typical multimeter.

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Figure 1-37. - A typical multimeter.

The multimeter shown in figure 1-37 may look complicated, but it is very easy to use. You have already learned about ammeters, voltmeters, and ohmmeters; the multimeter is simply a combination of these meters.

Most multimeters use a d'Arsonval meter movement and have a built-in rectifier for ac measurement. The lower portion of the meter shown in figure 1-37 contains the function switches and jacks (for the meter leads).

The use of the jacks will be discussed first. The COMMON or -jack is used in all functions is plugged into the COMMON jack. The +jack is used for the second meter lead for any of the functions printed in large letters beside the FUNCTION SWITCH (the large switch in the center). The other jacks have specific functions printed above or below them and are self-explanatory (the output jack is used with the dB scale, which will not be explained in this chapter). To use one of the special function jacks, except +10 amps, one lead is plugged into the COMMON jack, and the FUNCTION SWITCH is positioned to point to the special function (small letters). For example, to measure a very small current (20 microamperes), one meter lead would be plugged into the COMMON jack, the other meter lead would be plugged into the 50A AMPS jack, and the FUNCTION SWITCH would be placed in the 50V/IA AMPS position. To measure currents above 500 milliamperes, the +10A and -10A jacks would be used on the meter with one exception.

One meter lead and the FUNCTION SWITCH would be placed in the 10MA/AMPS position.

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Multimeter Controls

ultimeter Controls

As described above, the FUNCTION SWITCH is used to select the function desired; the -DC, +DC, AC switch selects dc or ac (the rectifier), and changes the polarity of the dc functions. To measure resistance, this switch should be in the +DC position.

The ZERO OHMS control is a potentiometer for adjusting the 0 reading on ohmmeter functions. Notice that this is a series ohmmeter. The RESET is a circuit breaker used to protect the meter movement (circuit breakers will be discussed in chapter 2 of this module). Not all multimeters have this protection but most have some sort of protection, such as a fuse. When the multimeter is not in use, it should have the leads disconnected and be switched to the highest voltage scale and AC. These switch positions are the ones most likely to prevent damage if the next person using the meter plugs in the meter leads and connects the meter leads to a circuit without checking the function switch and the dc/ac selector.

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Multimeter Scales

ultimeter Scales

The numbers above the uppermost scale in figure 1-38 are used for resistance measurement. If the multimeter was set to the R x 1 function, the meter reading would be approximately 12.7 ohms.

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the top and the numbers just below the scale are used for the 2.5-volt ac function only.

The lowest scale (labeled DB) will not be discussed. The manufacturer's technical manual will explain the use of this scale.

The table in figure 1-38 shows how the given needle position should be interpreted with various functions selected.

As you can see, a multimeter is a very versatile measuring device and is much easier to use than several separate meters.

PPPParallax Error

arallax Error

Most multimeters (and some other meters) have a mirror built into the scale. Figure 1-39 shows the arrangement of the scale and mirror.

Figure 1-39. - A multimeter scale with mirror.

The purpose of the mirror on the scale of a meter is to aid in reducing PARALLAX ERROR. Figure 1-40 will help you understand the idea of parallax.

Figure 1-40(A) shows a section of barbed wire fence as you would see it from one side of the fence. Figure 1-40(B) shows the fence as it would appear if you were to look down the fine of fence posts and were directly in line with the posts. You see only one post because the other posts, being in line,

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are hidden behind the post you can see. Figure 1-40(C) shows the way the fence would appear if you moved to the right of the line of posts. Now the fence posts appear to the right of the post closest to you. Figure 1-40(D) shows the line of fence posts as you would see them if you moved to the left of the front post. This apparent change in position of the fence posts is called PARALLAX.

Parallax can be a problem when you are reading a meter. Since the pointer is slightly above the scale (to allow the pointer to move freely), you must look straight at the pointer to have a correct meter reading. In other words, you must be in line with the pointer and the scale. Figure 1-41 shows the effect of parallax error.

Figure 1-41. - A parallax error in a meter reading. (A) shows a meter viewed correctly.

The meter reading is 5 units. Figure 1-41(B) shows the same meter as it would appear if you were to look at it from the right. The correct reading (5) appears to the right of the pointer because of parallax. The mirror on the scale of a meter, shown in figure 1-39, helps get rid of parallax error. If there is any parallax, you will be able to see the image of the pointer in the mirror. If you are looking at the meter correctly (no parallax error) you will not be able to see the image of the pointer in the mirror because the image will be directly behind the pointer. Figure 1-42 shows how a mirror added to the meter in figure 1-41 shows parallax error. Figure 1-42(A) is a meter with an indication of 5 units. There is no parallax error in this reading and no image of the pointer is seen in the mirror. Figure 1-42(B) shows the same meter as viewed from the right. The parallax error is shown and the image of the pointer is shown in the mirror.

Figure 1-42. - A parallax error on a meter with a mirrored scale.

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Multimeter Safety Precautions

ultimeter Safety Precautions

As with other meters, the incorrect use of a multimeter could cause injury or damage. The following safety precautions are the MINIMUM for using a multimeter.

Deenergize and discharge the circuit completely before connecting or disconnecting a multimeter.

Never apply power to the circuit while measuring resistance with a multimeter.

Connect the multimeter in series with the circuit for current measurements, and in parallel for voltage measurements.

Be certain the multimeter is switched to ac before attempting to measure ac circuits. Observe proper dc polarity when measuring dc.

When you are finished with a multimeter, switch it to the OFF position, if available. If there is no OFF position, switch the multimeter to the highest ac voltage position.

Always start with the highest voltage or current range.

Select a final range that allows a reading near the middle of the scale.

Adjust the "0 ohms" reading after changing resistance ranges and before making a resistance measurement.

Be certain to read ac measurements on the ac scale of a multimeter. Observe the general safety precautions for electrical and electronic devices.

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follows.

4. Complete the table below. Resistor

Number

Color- Code Value

Expected Value Measured Value % Error R1 R2 R3 R4 R5 R6 R7 R2 & R3 n.a. Nodes A - B n.a. Nodes C - D n.a. Nodes A - D n.a. From arrow - arrow n.a.

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Variable Resistors

Variable resistors can be wire-wound or the carbon type. Inside the metal case, the control has a circular disk that is carbon composition resistance element. It can be a thin coating pressed o a paper or a molded carbon disk. Joined to the two ends are the external soldering-lug terminals 1 and 3. The middle terminal is connected to the variable arm that contacts the resistor element by a metal spring wiper. As the shaft of the control is turned, the variable arm moves the wiper to make contact at different points in the resistor element. The same idea applies to the slide control, except that the resistor element is straight instead of circular.

When the contact moves closer to the end, the R decreases between this terminal and the variable arm. Between the two ends, however, the R is not variable but always has the maximum resistance of the control.

Carbon controls are available with a total R from 1000 Ω to 5 MΩ, approximately. Their power rating is usually ½ to 2 W.

Rheostats and Potentiometers

These are variable resistances, either carbon or wire-wound, used to vary the amount of current or voltage in a circuit. The controls can be used in either DC or AC applications.

A rheostat is a variable R with two terminals connected in series with a load. The purpose is to vary the amount of current.

A potentiometer, generally called a pot for short, has three terminals. The fixed maximum R across the two ends is connected across a voltage source. The variable arm is used to vary the voltage division between the center terminal and the ends. This function of a potentiometer is compared with a rheostat in the table below.

Rheostat Potentiometer

Two terminals Three terminals

In series with load and V source

Ends are connected across V source

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This symbol is used to indicate a variable resistor in a circuit diagram.

can be seen on the far right. Its value is very easy to adjust.

The four resistors at the center of the photograph are the semi-fixed type. These ones are mounted on the printed circuit board.

The two resistors on the left are the trimmer potentiometers.

There are three ways in which a variable resistor's value can change according to the rotation angle of its axis.

When type "A" rotates clockwise, at first, the resistance value changes slowly and then in the second half of its axis, it changes very quickly. The "A" type variable resistor is typically used for the volume control of a radio, for example. It is well suited to adjust a low sound subtly. It suits the characteristics of the ear. The ear hears low sound changes well, but isn't as sensitive to small changes in loud sounds. A larger change is needed as the volume is increased. These "A" type variable resistors are sometimes called "audio taper" potentiometers.

As for type "B", the rotation of the axis and the change of the resistance value are directly related. The rate of change is the same, or linear, throughout the sweep of the axis. This type suits a resistance value adjustment in a circuit, a balance circuit and so on. They are sometimes called "linear taper" potentiometers. Type "C" changes exactly the opposite way to type "A". In the early stages of the rotation of the axis, the resistance value changes rapidly, and in the second half, the change occurs more slowly. This type isn't too much used. It is a special use.

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Section 2.6 Rating of Resistors

In addition to having the required ohms value, a resistor should have a wattage rating high enough to dissipate the power produced by the current flowing through the resistance, without becoming too hot. Carbon resistors in normal operation are quite warm, up to a maximum temperature of 85°C, which is close to 100°C boiling point of water. Carbon resistors should not be so hot, however that they “sweat” beads of liquid on the insulating case. Wire-wound resistors operate at very high temperatures, a typical value being 300°C for the maximum temperature. If a resistor becomes too hot because of excessive power dissipation, it can change appreciably in resistance value or burn open.

The power rating is a physical property that depends on the resistor construction. Note the following:

1. A larger physical size indicates a higher power rating.

2. Higher-wattage resistors can operate at higher temperatures.

3. Wire-wound resistors are physically larger with higher wattage ratings than carbon resistors.

Section 2.7 Resistor Troubles

The most common trouble in resistors is an open circuit. When the open resistor is a series component, there is no current in the entire path.

Noisy controls. In applications such as volume and tone control, carbon controls are preferred because the smoother change in resistance results in less noise when the variable arm is rotated. With use, however, the resistance element becomes worn by the wiper contact, making the control noisy. When a volume or tone control makes a scratchy noise as the shaft is rotated, it indicates a worn out resistance element.

Checking resistors with ohmmeter. Resistance measurements are made with an ohmmeter. The ohmmeter has its own voltage source so that it is always used without any external power applied to the resistance being measured. Separate the resistance from the circuit by disconnecting one lead of the resistor. Then connect the ohmmeter lead across the resistance to be measured

An open resistor reads indefinitely high ohms. For some reason, an infinite ohm is often confused with zero ohms. Remember, though, that an infinite ohm means an open circuit. The current is zero, but the resistance is infinitely high. Furthermore it is practically impossible for a resistor to become short-circuited in itself. The resistor may be short-circuited by some other part of the circuit. However, he construction of resistors such that the trouble they develop is an open circuit with infinitely high ohms.

The ohmmeter must have an ohms scale capable of reading the resistance value, or the resistor cannot be checked. In checking a 10 MΩ resistor, for instance, if the highest R the ohmmeter can read is 1 MΩ, it will indicate infinite resistance, even if the resistors’ normal value is 10 MΩ. An ohms scale of 100 MΩ or more should be used for checking such resistances.

To check resistors of less than 10 Ω, a low ohms scale of about 100 Ω or less is necessary. Center scale should be 6 Ω or less. Otherwise, the ohmmeter can read a normally low resistance value as zero ohms.

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reason is that the total physical size increases with each added resistor. Equal resistors are generally used in order to have equal distribution of I, V and P.

In general, series resistors add for a higher RT. With parallel resistors, REQ is reduced.

Series Combinations of Resistors

Two elements are said to be in series whenever the same current physically flows through both of the elements. The critical point is that the same current flows through both resistors when two are in series. The particular configuration does not matter. The only thing that matters is that exactly the same current flows through both resistors. Current flows into one element, through the element, out of the element into the other element, through the second element and out of the second element. No part of the current that flows through one resistor "escapes" and none is added. This figure shows several different ways that two resistors in series might appear as part of a larger circuit diagram.

You might wonder just how often you actually find resistors in series. The answer is that you find resistors in series all the time.

An example of series resistors is in house wiring. The leads from the service entrance enter a distribution box, and then wires are strung throughout the house. The current flows out of the distribution box, through one of the wires, then perhaps through a light bulb, back through the other wire. We might model that situation with the circuit diagram shown below.

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In many electronic circuits series resistors are used to get a different voltage across one of the resistors. We'll look at those circuits, called voltage dividers, in a short while. Here's the circuit diagram for a voltage divider.

Besides resistors in series, we can also have other elements in series - capacitors, inductors, diodes. These elements can be in series with other elements. For example, the simplest form of filter, for filtering low frequency noise out of a signal, can be built just by putting a resistor in series with a capacitor, and taking the output as the capacitor voltage.

As we go along you'll have lots of opportunity to use and to expand what you learn about series combinations as you study resistors in series.

Let's look at the model again. We see that the wires are actually small resistors (small value of resistance, not necessarily physically small) in series with the light bulb, which is also a resistor. We have three resistors in series although

two of the resistors are small. We know that the resistors are in series because all of the current that flows out of the distribution box through the first wire also flows through the light bulb and back through the second wire, thus meeting our condition for a series connection. Trace that out in the circuit diagram and the pictorial representation above.

Let us consider the simplest case of a series resistor connection, the case of just two resistors in series. We can perform a thought experiment on these two resistors. Here is the circuit diagram for the situation we're interested in.

Imagine that they are embedded in an opaque piece of plastic, so that we only have access to the two nodes at the ends of the series connection, and the middle node is inaccessible. If we measured the resistance of the combination, what would we find? To answer that question we need to define voltage and current variables for the resistors. If we take advantage of the fact that the current through them is the same (Apply KCL at the interior node if you are unconvinced!) then we have the situation below.

Note that we have defined a voltage across each resistor (Va and Vb) and current that flows through both resistors (Is) and a voltage variable, Vs, for the voltage that appears across the series combination.

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Vs= Is Ra + Is Rb Vs= Is (Ra + Rb) Vs= Is Rseries

Here, we take Rseries to be the series equivalent of the two resistors in series, and the expression for

Rseries is:

Rseries = Ra + Rb

What do we mean by series equivalent? Here are some points to observe. If current and voltage are proportional, then the device is a resistor.

We have shown that Vs= Is X Rseries, so that voltage is proportional to current, and the constant

of proportionality is a resistance.

We will call that the equivalent series resistance.

There is also a mental picture to use when considering equivalent series resistance. Imagine that you have two globs of black plastic. Each of the globs of black plasic has two wires coming out. Inside these two black plastic globs you have the following.

In the first glob you have two resistors in series. Only the leads of the series combination are available for measurement externally. You have no way to penetrate the box and measure things at the interior node.

In the second box you have a single resistor that is equal to the series equivalent. Only the leads of this resistor are available for measurement externally.

Then, if you measured the resistance using the two available leads in the two different cases you would not be able to tell which black plastic glob had the single resistor and which one had the series combination.

Here are two resistors. At the top are two 2000W resistors. At the bottom is single 4000W resistors. (Note, these are not exactly standard sizes so it took a lot of hunting to find a supply store that sold them!). You can click the green button to grow blobs around them.

After you have grown the blobs around the resistors there is no electrical measurement you can make that will allow you to tell which one has two resistors and which one has one resistor. They are electrically indistinguishable! (Or, in other words, they are equivalent!)

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Here is a circuit you may have seen before. Answer the questions below for this circuit.

1.Are elements #3 and #4 in series? (Yes or No) 2.Are elements #1 and #2 in series? (Yes or No) 3.Is the battery in series with any element?

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Element 1

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Element 2

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Element 3

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Element 4

4.Is the series equivalent resistor larger than either resistor, or is it smaller? (Larger or Smaller) 5. What is the series equivalent of two 1000 W resistors in series?

6. What is the series equivalent of a 1000 W resistor and a 2700 W resistor in series?

7. What is the series equivalent of three 1000 W resistors in series? You may want to do this problem in two steps.

8. Imagine that you have a 100 W resistor. You want to add a resistor in series with this 100 W resistor in order to limit the current to 0.5 amps when 110 volts is placed across the two resistors in series. How much resistance should you use?

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Note that we have defined the voltage across both resistor (Vp) and the current that flows through each resistor (Ia and Ib) and a voltage variable, Vp, for the voltage that appears across the parallel combination.

Let's list what we know.

The voltage across the two resistors is the same. The current through the parallel combination is given by:

Ip= Ia + Ib

The currents through the two resistors are given by Ohm's Law: Ia = Vp /Ra

Ib = Vp /Rb

We can combine all of these relations, and when we do that we find the following. Ip= Ia + Ib

Ip= Vp /Ra + Vp /Rb

Ip= Vp[ 1/Ra + 1/Rb]

Ip= Vp/Rparallel

Here, we take Rparallel to be the parallel equivalent of the two resistors in parallel, and the expression

for Rparallel is:

1/Rparallel = 1/Ra + 1/Rb

There may be times when it is better to rearrange the expression for Rparallel. The expression can be rearranged to get:

Rparallel = (Ra*Rb)/(Ra + Rb)

Either of these expressions could be used to compute a parallel equivalent resistance. The first has a certain symmetry with the expression for a series equivalent resistance.

Parallel Resistors

Parallel Resistors ---- A Point to Remember

A Point to Remember

It is important to note that the equivalent resistance of two resistors in parallel is always smaller than either of the two resistors.

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1. Is the parallel equivalent resistor larger than either resistor, or is it smaller? 2. What is the parallel equivalent of two 1000 W resistors in parallel?

3. What is the parallel equivalent of a 1000 W resistor and a 1500 W resistor in parallel?

4. What is the equivalent of three 1000 W resistors in parallel? You may want to do this problem in two steps.

5.What is the equivalent resistance of this resistance combination?

6. What is the equivalent resistance of this resistance combination?

7. What is the equivalent resistance of this resistance combination? Here all three resistors are 33 kW. Remember to input your answer in ohms.

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is a resistor. It has two leads at the left (marked here with red dots) and we'll assume that we want to find the equivalent resistance you would have at those leads.

We will use the following numerical values for the resistors in this example, and we will work through using these values.

Ra = 1500 W Rb = 3000 W Rc = 2000 W Rd = 1000 W Vs = 12 v

We need to figure out where we can start. We can start by trying to find any of the combinations we've learned about. So let's think about whether there are any series or parallel combinations and if there are let's see if we can identify them. Then we can apply what we know about series and parallel combinations. There's no guarantee that approach will work, but it is worth a try. Let's look at two resistors at a time.

Now, we should be able to replace the two resistors in series with their series equivalent. If we do that, there's a node in the middle with a voltage, and we'll lose information about that voltage. Right now, we're not interested in that voltage, and we'll willing to lose that information. Let's just replace the two resistors with their series equivalent. Click the red button to make that replacement. Depressing the button will remove the two resistors in series, and releasing the button will insert the replacement.

Now you should have the circuit with the two resistors in series replaced by their series equivalent. Now, we can see that there is another replacement we can make. What's that replacement?

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Ok, you see how it goes. Let's take a numerical example using the values mentioned above. Ra = 1500 W Rb = 3000 W Rc = 2000 W Rd = 1000 W Vs = 12 v

Here is the circuit.

1. What is the equivalent resistance of the two resistors in series - 1000W and 2000W? 2. Next you should have two resistors in parallel. What is the parallel equivalent?

3. Now you should have two resistors in series attached to the source. What is the value of the series equivalent?

4. With a 12v source - as shown in the figure - what is the current that is drawn from the source? Give your answer in amperes here. Give your answer in milliamperes here, if that's what you want.

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Please answer what is asked.

1.) If a current of 3 A is divided by the following circuit, the current flowing through the 4 Ohm resistor is

a. 3 b. 2 c. 1 d. 1.5

2.) The diagram at the right shows part of a circuit into which a current I is flowing. Which ammeter shows the highest reading?

a. A1 b. A2 c. A3

d. All three ammeters give the same reading 3.) The diagram to the right represents a part of a

circuit containing an ohmic resistor, a voltmeter and an ammeter. If the reading on the ammeter A increases the reading on voltmeter V …

a. increases in the same ratio b. increases but not in the same ratio c. remains unchanged

d. decreases in the same ratio

4.) A battery is connected to two identical light bulbs in parallel as well as another identical bulb in series. An ammeter and a voltmeter are also connected as shown in the circuit diagram below.

Voltmeter reading Ammeter reading a increases increases

b increases decreases

c increases unchanged

d decreases decreases

5.) A learner connects a circuit as shown in the diagram to the right. He/she uses a source of electricity with an electromotive force (emf) of 12 V. Which one of the following best gives the ammeter and voltmeter readings which the learner is most likely to get with this circuit?

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Ammeter reading Voltmeter reading a reads zero reads zero b reads zero reads 12 V c very large reading reads zero d very large reading reads 12 V

6.) Three identical resistors of 4 Ω are connected to give a combined resistance of 6 Ω. Which of the following circuit diagrams illustrates how this was done?

a. I b. II c. III d. IV

7.) In the circuit to the right B1, B2 and B3 are identical light bulbs. The internal resistance of the

battery can be ignored.

Which statement is true regarding the relative brightness of the bulbs?

a. The three bulbs glow with the same brightness.

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X Y a. brighter brighter b. dimmer dimmer c. brighter not lit up d. not lit up brighter

9.) A student connects three identical resistors as shown in the sketch to the right. The potential difference across the battery is 12 Volt. What are the readings on V1 and V2 respectively?

V1 V2

a. 4 8

b. 6 6

c. 8 4

d. 9 3

10.) A 9 V battery is composed of six 1,5 V cells, which are connected in series. Each cell has an internal resistance of 0,2 Ω. What is the highest current that can be obtained from such a battery?

a. 7.5A b. 1.5A c. 1.2A d. 0.3A

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Exercises on resistor connections.

Find total resistance RT given the following circuits

1. Series connection. a. Solution: RT = R1 + R2 + R3 = 1KΩ + 5KΩ + 10KΩ = 16KΩ b. Solution: RT = R1 + R2 + R3 = 1MΩ + 5KΩ + 100KΩ = 1MΩ + .005MΩ + .1MΩ = 1.101MΩ or RT = R1 + R2 + R3 = 1MΩ + 5KΩ + 100KΩ = 1000KΩ + 5KΩ + 100KΩ = 1101KΩ 2. Parallel connection. a.

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c.

3. Simple Series-Parallel

a.

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OHM'S LAW

What is Ohm’s Law

What is Ohm’s Law????

A

simple relationship exists between voltage, current, and resistance in electrical circuits. Understanding this relationship is important for fast, accurate electrical problem diagnosis and repair. Ohm's Law says: The current in a circuit is directly proportional to the applied voltage and inversely proportional to the amount of resistance. This means that if the voltage goes up, the current flow will go up, and vice versa. Also, as the resistance goes up, the current goes down, and vice versa. Ohm's Law can be put to good use in electrical troubleshooting. But calculating precise values for voltage, current, and resistance is not always practical ... nor, really needed. A more practical, less time-consuming use of Ohm's Law would be to simply apply the concepts involved:

SOURCE VOLTAGE is not affected by either current or resistance. It is either too low, normal, or too high. If it is too low, current will be low. If it is normal, current will be high if resistance is low, or current will be low if resistance is high. If voltage is too high, current will be high.

CURRENT is affected by either voltage or resistance. If the voltage is high or the resistance is low, current will be high. If the voltage is low or the resistance is high, current will be low.

RESISTANCE is not affected by either voltage or current. It is either too low, okay, or too high. If resistance is too low, current will be high at any voltage. If resistance is too high, current will be low if voltage is okay.

NOTE: When the voltage stays the same, such as in an Automotive Circuit... current goes up as resistance goes down, and current goes down as resistance goes up. Bypassed devices reduce resistance, causing high current. Loose connections increase resistance, causing low current.

C H A P T E R

+ + + +

3-1 Ohm’s Law Formula

3-2 Applications of Ohm’s Law

Current, Voltage and Resistance Calculations in:

3-3 Series Circuits

3-4 Parallel Circuits

3-5 Series Parallel Circuits

3-6 Voltmeters

3-7 Ammeters

3-8 Problem Sets on Ohm’s Law + + + +

3

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Section 3.1 Ohm’s Law Formula

When voltage is applied to an electrical circuit, current flows in the circuit. The following special relationship exists among the voltage, current and resistance within the circuit: the size of the current that flows in a circuit varies in proportion to the voltage which is applied to the circuit, and in inverse proportion to the resistance through which it must pass. This relationship is called Ohm's law, and can be expressed as follows:

E = I R

Voltage = Current x Resistance E Voltage applied to the circuit, in volts (V) I Current flowing in the circuit, in amperes (A) R Resistance in the circuit, in ohms

In practical terms "V = I x R" which means "Voltage = Current x Resistance". 1 volt will push one amp through 1 ohm of resistance.

NOTE: E = IR, V=AR, or V=IR are all variations of the same formula. How you learned Ohm's law will determine which one you will use. Personal preference is the only difference; anyone will get you the correct answer.

OHM'S LAW SYMBOL SHORTCUT

Mathematical formulas can be difficult for many who don't use them regularly. Most people can remember a picture easier than a mathematical formula. By using the Ohms law symbol below, anyone can remember the correct formula to use. By knowing any two values you can figure out the third. Simply put your finger over the portion of the symbol you are trying to figure out and you have your formula.

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Section 3.2 Application of Ohm’s Law

As an application of Ohm's law, any voltage V, current I or resistance R in an electrical circuit can be determined without actually measuring it if the two others values are known.

This law can be used to determine the amount of current I flowing in the circuit when voltage V is applied to resistance R. As stated previously, Ohm's law is:

Current = Voltage / Resistance.

In the following circuit, assume that resistance R is 2 and voltage V that is applied to it is 12 V. Then, current I flowing in the circuit can be determined as follows:

This law can also be used to determine the voltage V that is needed to permit current I to pass through resistance R: V = I x R (Voltage= Current x Resistance).

In the following circuit, assume that resistance R is 4 ohms. The voltage V that is necessary to permit a current I of 3 A to pass through the resistance can be determined as follows:

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Still another application of the law can be used to determine the resistance R when the voltage V which is applied to the circuit and current I flowing in the circuit are already known:

In the following circuit, assume that a voltage V of 12 V is applied to the circuit and current I of 4 A flows in it. Then, the resistance value R of the resistance or load can be determined as follows:

TYPES OF CIRCUITS

Individual electrical circuits normally combine one or more resistance or load devices. The design of the automotive electrical circuit will determine which type of circuit is used. There are three basic types of circuits:

Series Circuit Parallel Circuit

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Section 3.3 Series Circuits

A series circuit is the simplest circuit. The conductors, control and protection devices, loads, and power source are connected with only one path to ground for current flow. The resistance of each device can be different. The same amount of current will flow through each. The voltage across each will be different. If the path is broken, no current flows and no part of the circuit works. Christmas tree lights are a good example; when one light goes out the entire string stops working.

A Series Circuit has only one path to ground, so electrons must go through each component to get back to ground. All loads are placed in series.

Therefore:

1. An open in the circuit will disable the entire circuit. 2. The voltage divides (shared) between the loads. 3. The current flow is the same throughout the circuit. 4. The resistance of each load can be different.

SERIES CIRCUIT CALCULATIONS

If, for example, two or more lamps (resistances R1 and R2, etc.) are connected in a circuit as follows, there is only one route that the current can take. This type of connection is called a series connection. The value of current I is always the same at any point in a series circuit.

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The combined resistance RO in this circuit is equal to the sum of individual resistance R1 and R2. In other words: The total resistance(RO) is equal to the sum of all resistances (R1 + R2 + R3 + ...)

Therefore, the strength of current (I) flowing in the circuit can be found as follows:

Resistance R0 (a combination of resistances R1 and R2, which are connected in series in the circuit as illustrated) and current I flowing in this circuit can be determined as follows:

VOLTAGE DROP

A voltage drop is the amount of voltage or electrical pressure that is used or given up as electrons pass through a resistance (load). All voltage will be used up in the circuit. The sum of the voltage drops will equal source voltage. A voltage drop measurement is done by measuring the voltage

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before entering the load and the voltage as it leaves the load. The difference between these two voltage readings is the voltage drop.

VOLTAGE DROP TOTAL

When more than one load exists in a circuit, the voltage divides and will be shared among the loads. The sum of the voltage drops equal source voltage. The higher the resistance the higher the voltage drop. Depending on the resistance, each load will have a different voltage drop.

0V + 5V + 7V + 0V = 12V

VOLTAGE DROP CALCULATION

When current flows in a circuit, the presence of a resistance in that circuit will cause the voltage to fall or drop as it passes through the resistance. The resultant difference in the voltage on each side of the resistance is called a voltage drop. When current (I) flows in the following circuit, voltage drops V1 and V2 across resistances R1 and R2 can be determined as follows from Ohm's law. (The value of current I is the same for both R1 and R2 since they are connected in series.)

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The sum of the voltage drops across all resistances is equal to the voltage of the power source (VT):

The voltage drop across resistances R1 and R2 in the following circuit can be determined as follows:

Section 3.4 PARALLEL CIRCUIT

A parallel circuit has more than one path for current flow. The same voltage is applied across each branch. If the load resistance in each branch is the same, the current in each branch will be the same. If the load resistance in each branch is different, the current in each branch will be different. If one branch is broken, current will continue flowing to the other branches.

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A Parallel Circuit has multiple paths or branches to ground. Therefore:

1. In the event of an open in the circuit in one of the branches, current will continue to flow through the remaining.

2. Each branch receives source voltage.

3. Current flow through each branch can be different. 4. The resistance of each branch can be different.

In parallel connection, two or more resistances (R1, R2, etc.) are connected in a circuit as follows, with one end of each resistance connected to the high (positive) side of the circuit, and one end connected to the low (negative) side. Full battery voltage is applied to all resistances within a circuit having a parallel connection.

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The total current I is also equal to the sum of currents I1 and I2 flowing through individual resistances R1 and R2

Since battery voltage V is applied equally to all resistances, the strength of currents I1 and I2 can be determined from Ohm's law as follows:

Resistance RO (a combination of resistances R1 and R2, which are connected in parallel in the circuit as shown below), the total current I flowing in the circuit, and currents I1 and I2 flowing through resistances R1 and R2, can be determined respectively as follows:

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Section 3.5 Series - Parallel Circuits

A series-parallel circuit has some components in series and others in parallel. The power source and control or protection devices are usually in series; the loads are usually in parallel. The same current flows in the series portion, different currents in the parallel portion. The same voltage is applied to parallel devices, different voltages to series devices. If the series portion is broken, current stops flowing in the entire circuit. If a parallel branch is broken, current continues flowing in the series portion and the remaining branches.