FINAL DATA SHEET
Table 2.1 (Measured Values)
R1 R2 R3 R4 R5 RT
0.988kΩ 0.980kΩ 469.8kΩ 0.681kΩ 0.670kΩ 2.319kΩ
V1 V2 V3 V4 V5 VT
6.35V 6.291V 2.24V 1.136V 1.118V 14.91V
I1 I2 I3 I4 I5 IT
6.5mA 6.5mA 4.8mA 1.9mA 1.9mA 6.5mA
R1 R2 R3 R4 R5 RT 976.92Ω 967.85Ω 466.67Ω 597.89Ω 588.42 2293.85Ω MEASURED VALUES CALCULATED VALUES
SAMPLE CALCULATIONS Calculated Values:
DISCUSSION
The analysis of an electrical network consists of determining each of the unknown branch currents and node voltages. A number of methods for network analysis have been developed, based on Ohm’s Law and Kirchhoff’s Law.
Resistive circuits may be analyzed by combining networks of parallel and series resistances into a single equivalent resistance, then using Ohm’s Law to find the current or voltage across that equivalent resistance. Once this is known, it is possible to work backward and use Ohm’s Law to calculate the voltage and current across any resistance in the network.
Ohm’s Law deals with the relationship between voltage and current in ideal conductor. The relationship states that: The potential difference (voltage) across an ideal conductor is proportional to the current through it. The constant of proportionality is called the ‘resistance’ R. Mathematically speaking: V=IR, where V is the potential difference between two points which include a resistance R. I is the current flowing through the resistance. Ohm’s law can be used to solve simple circuits. A complete circuit is one which is a closed loop. It is formed when a conductive path is created to allow free electrons to continuously move. This continuous movement of free electrons through the conductors of a circuit is called a current. The force motivating the electrons to flow in a circuit is called voltage. The sum of the voltages around a complete circuit is zero.
Current is a flow of electrical charge carriers, usually electrons. The standard unit is the ampere, symbolized by A. Electric current can be either direct or alternating. Direct current (DC) flows in the same direction at all points in time, although the instantaneous magnitude of the current might vary. In an alternating current (AC), the flow of charge carriers reverses direction periodically. Resistance is the opposition that a substance offers to the flow of electric current. The standard unit of resistance is the ohm . In general, when the applied voltage is held constant, the current is a DC electrical circuit is inversely proportional to the resistance. If the resistance is doubled, the current is cut in half; if the resistance is halved, the current is doubled. Voltage, also called electromotive force, is a quantitative expression of the potential difference in charge between two points in an electric field. The greater the voltage, the greater the flow of electrical current through a conducting or semi-conducting medium for a given resistance of the flow.
Components of an electrical circuit can be connected in many ways. The two simplest of these are called series and parallel. In a series circuit, it provides only one complete path where current could flow wherein the resistors are simply connected end to end. It may also be defined as a circuit that provides only one path for current between two points in a circuit so that the same current flows through each series resistors. Observations regarding resistances in series can be summarized in 3 rules: i. The current in all parts of the series circuit has the same magnitude. ii. The sum of all the separate drops in a potential around a series circuit is equal to the applied emf. iii. The total resistance in a series circuit is equal to the sum of all the separate resistances.
In a parallel circuit, it is described as a circuit connection of two or more resistors that are connected between the same two node or points. A parallel circuit provides more than one path for the current. Each current path is called a branch. Observations regarding resistances in parallel can be summarized in 3 rules: i. The total current in a parallel circuit is equal to the sum of the currents in the separate branches. ii. The total potential difference across all branches of a parallel circuit must have the same magnitude, iii. The reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the separate resistances in parallel.
CONCLUSION
In experiment 2, Analysis of Resistive Network: Series-Parallel Circuits, the group was able to determine the difference between series and parallel circuit. In a series circuit, the current is constant at any resistor and is equal to the total current in the circuit while in a parallel circuit, the total current in a parallel circuit is equal to the sum of the currents in the separate branches. Voltage is constant in a parallel circuit and its total resistance is equal to the reciprocal of the sum of the reciprocals of the individual resistance. In a series circuit, the total resistance is equal to the sum of the individual resistances and the total voltage is also equal to the sum of the individual voltages across the circuit. Mathematically speaking, for Series Circuit:
For Parallel Circuit:
( )
From the result of the experiment, the group got 2319 as the measured value of resistance, while the computed value was 2293.85 with 1.1% difference. Probable cause of error might be from human mistakes in reading the ammeter. Instrumental errors are also a factor.
During the experiment, the group took so much time getting resistors with values that are somewhat close to each other and for that reason it is suggested that before the start of the experiment, the resistors should be arranged in order of their resistive values.
ANSWERS/SOLUTIONS TO PROBLEMS
1. What are the identifying characteristics of a series circuit?
The three characteristics of a series circuit are as follows: The current flow is constant throughout the circuit, there is voltage drop across each component on the circuit and lastly, there is the linear flow of electrons.
2. What are the identifying characteristics of a parallel circuit?
A parallel circuit has two or more paths for current to flow through, hence of one of the parallel paths is broken, current will continue to flow in all the other parts. The voltage is the same across each component of the parallel circuit. Finally, the sum of the currents through each path is equal to the total current that flows from the source.
3. What changes occur in the total resistance of a circuit as additional resistances are added (a) in series, (b) in parallel?
Resistance added in series always adds up together increasing the total resistance of the circuit. For series circuits, RT = R1 + R2 + R3 + … + Rn.
Conversely, adding parallel resistance reduces the total resistance of the circuit. The easiest way to determine the parallel resistance is to add the inverse of resistance which is conductance. For parallel circuits, RT = (1/R1 + 1/R2 + 1/R3 + … + 1/Rn)-1.
4. What are the different types of resistances and their purpose?
a. Fixed Resistors – are used in situations where an electrical circuit may need a lesser amount of current to flow through it than the input value.
i. Carbon Composition Resistors - composed by a mixture of carbon granules and powdered ceramic. The resistor value depends of the composition of the ceramic material. A higher quantity of ceramic content will result in more resistance. This is often used in power supply and welding circuit.
ii. Carbon Film Resistors - are formed by depositing a carbon film layer on an insulating substrate. Helical cuts are then made through the carbon film to trace a long and helical resistive path. The resistance can be varied by using different resistivity carbon material and modifying the shape of the resistor. The helical resistive path make these resistors highly inductive and of little use for RF applications. The operation of these resistors requires high pulse stability.
iii. Metal Film Resistors - are made from small rods of ceramic coated with metal or metal oxide. The value of resistance is controlled mainly by the thickness of the coating layer (the thicker the layer, the lower is the value of resistance). These have much better temperature stability than their carbon equivalents, lower noise and are generally better for high frequency or radio frequency applications.
iv. Wire Wound Resistors - vary in size and physical appearance. Their resistive elements are commonly length of wire wrapped around a small ceramic or glass fiber rod and coated in an insulating flameproof cement film. They are normally available in low values of resistance but are capable of dissipating large amounts of power but gets very hot during use, thus, fireproof cases or coatings are vital.
v. Thin Film Resistors - are made by sputtering the resistive
material onto an insulating substrate. These are usually more expensive than thick film resistors and are typically used in high precision measuring or monitoring equipments.
vi. Surface Mount Resistors - help to achieve very low power
dissipation along with very high component density. These are made by depositing a film of resistive material on a tiny
ceramic chip.
vii. Network Resistors - are the combination of resistances which may be giving the identical value at all pins, with one pin acting as a a common terminal. These are available in both single line package and dual in line package and may be surface mount or through hole. These are used in applications such as pull
b. Variable Resistors – are the combination of resistances which may be giving the identical value of all pins, with one pin acting as a common terminal. These are available in both single line package and dual in line package and may be surface mount or through hole. These are used in applications such as pull up/down, DAC, etc.
i. Potentiometers are a 3-terminal variable resistor. It has wide use in circuits for a variety of uses but their main function is to increase or decrease the amplitude of a signal circuit.
ii. Rheostats are a 2-terminal variable resistor. Just like potentiometers, rheostats can be used to vary AC or DC signals.
iii. Thermistors are a thermally sensitive resistor whose resistance value changes with changes in operating temperature. Thermistors are frequently used in electronic circuits that handle temperature measurement, temperature control, and temperature compensation.
iv. Photoresistors are resistors whose resistance values change according to the light striking the surface of the resistor.
5. Why are lamps in a house lighting circuit not connected in series?
Because lamps are rated in voltage and if the lighting circuit is connected in series then the lamps would have to share the voltage, each would only get (Voltage / no. of lamps) each. If just one of the lamps burned out, all of it would go out. That is why it is better that the connection is in parallel, so that it can be easily controlled separately.
6. A small lamp is designed to draw 300mA in a 6V circuit. What is the resistance of the lamp filament?
7. A battery with an internal resistance of 1.5 is connected in series with resistors R1 = 3Ω and R2 = 3.5Ω if the potential difference across the 3Ω resistor is 9V. What is the emf of the battery?
8. Determine the ideal voltage source needed by three resistors connected in series R1 = 6 Ω, R2 = 8 Ω, and R3 = 10 Ω if a required current of 0.5A flows in the circuit.
R3 and R4 are in series
R3,4 = R3 + R4 = 4.5 Ω + 1.5 Ω = 6 Ω
R7 and R8 are in series
R7,8 = R7 + R8 = 5 Ω + 25 Ω = 30 Ω
R10 and R12 are in parallel
(
)
( )
R11 and R10,12 are in series
R10,11,12 = RA = 4 +8 = 12
RA and R3,4 are in parallel
(
)
=( )
RB and R5 are in series
RB,5 and R9 are in parallel ( ) ( )
RC and R2 are in series
RC,2 = RD = RC+R2 = 6 +14 = 20
RD and R7,8 are in parallel
( ) ( )
R1, RE and R6 are in series
R1,E,6 = RT = 12Ω + 1Ω + 2Ω = 15Ω
REFERENCES: http://www3.eng.cam.ac.uk/DesignOffice/mdp/electric_web/DC/DC_5.html https://www.swtc.edu/ag_power/electrical/lecture/parallel_circuits.htm http://en.wikipedia.org/wiki/Series_and_parallel_circuits http://www.learningaboutelectronics.com/Articles/Types-of-resistors http://www.engineersgarage.com/tutorials/resistors http://www.electronics-tutorials.ws/resistor/res_1.html
