Experiment 8: Series/Parallel Circuit Elements Laboratory Report
Frances Aina Beatrice Javier, Faith Dominique Lee, Ian Carlos Lipardo, Joy Clarize Lubao
Department of Math and Physics
College of Science, University of Santo Tomas Espana, Manila Philippines
Abstract
In this experiment, the resistance of two resistors in a parallel and series circuit was found based on its color code and using the ammeter and a voltmeter to detect its current and voltage. The series circuit yielded a total resistance of 437Ω with a 1.63% error while the parallel circuit yielded a total resistance of 77.6 Ω with a 0.9% error. The internal resistance of a battery cell was also found, having an internal resistance of 77.8 Ω.
1. Introduction
“Hey, girl. Can you feel that? What?
The connection between you and me.” Despite being poorly written, the pun above basically expresses the relationship of the circuits- connection. Like relationships, which usually have love, way of communication and fights, circuits also have three basic components, which are a source of electrical potential difference, a
conductive path, and an electrical resistance. The source of electrical potential difference, usually a battery, is commonly a chemical storage device capable of making a reaction in which electrons are produced. A conductive path allows the movement of these charges, which typically made out of wires. An electrical resistance is loosely defined as any object that uses electricity to work, which is almost every electrical appliance out there. There are two kinds of circuits: series circuit and parallel circuit. A series circuit has more than one resistor and has only one path for the charges to move along. If one bulb burned out, the whole string of lights went off. Series circuits are known to have the same current all throughout. On the other hand, parallel circuits are known to have the same voltage throughout its course. By the time the current reaches the resistors, it would have already split into two different currents since the path to the resistors splits; however, it does not necessarily mean the current split in half. Having known the two circuits’ nature, this experiment aims to determine the
resistance of a resistor based on its color code and to verify the laws on series and parallel resistors and its cells. 2. Theory
A series circuit is done when two or more resistors are connected in one path. The total current (IT) flowing in this
connection is constant. This can be described by the following equation:
IT = I1 = I2 = I3…
The total (VT) voltage in the
circuit is equal to the sum of the individual potential energies in the circuit. This can be described by the following equation:
VT = V1 + V2 + V3…
When Ohm’s Law is applied the equation then becomes:
V = IR
V1 = I1R1 V2 = I2R2 V3 = I3R3 …
The sum of the resistance is the total resistance (RT) of the circuit
described by the equation: RT = R1 + R2 + R3…
Electricity flows in two or more paths in a parallel circuit. These paths recombine to complete the circuit. Each load in the path/s receive/s the full circuit voltage.
In a parallel circuit, the voltage across each of the loads is equal as seen in the equation:
V = V1 = V2 = V3 = VN
The sum of all currents in each resistor is equal the combined currents added together:
IT = I1 + I2 + I3 + IN
Ohm’s Law gives the formulas for the individual resistance in the circuit:
I1=V R1
I2= V R2 I3=V R3
IT= V RT
The reciprocal of the total resistance of a parallel circuit (RT) is
equal to the sum of the reciprocals of each resistor in parallel:
1 RT= 1 R1= 1 R2= 1 R3
3. Methodology
Experiment 8: Series/Parallel Circuit Elements required the use of the following materials:
Activity 1 deemed the use of the resistors, power source and the voltmeter/ammeter. The values of two resistors were determined and recorded as R1 and R2. The resistors were
connected in series to the power source. Using the voltmeter and ammeter, the current and voltage drop were recorded across each resistor. The total current and total voltage were also measured along the combination. The total experimental and theoretical resistance were computed. The % error was determined as well.
Activity 2 is very similar to the first activity, but this time the resistors were connected in parallel.
Activity 3 required the use of a cell (9V battery) and the voltmeter/ammeter. The electromotive force of the cell was determined by connecting the voltmeter across terminals. A known resistance (R) was connected in series with the cell. The current (I) delivered to the circuit is measured by an ammeter. The internal resistance (r) of the cell was computed. Resistor Voltmeter /Ammeter 9V Battery Power source
4. Results and Discussion
Voltage (V) Current (I)
R1=10X101±5% 2.3 23 A
R2=33X101±5% 7.7 23 A
Theoretical RT= 408Ω-452Ω
Experimental RT= 437Ω
% Error= 1.63%
Table 1. Summary of Data for Series Wiring The first activity in experiment 8 involves the two objectives of the experiment: (1) to determine the resistance of a resistor based on its color code; (2) to verify the laws on series/parallel. In this activity, the value of the two resistors that were used was computed using the color code
corresponding to each. The color code of each was observed to be painted on each resistor. Each color has a given value. Using the table of values for each color, the value of each resistor was recorded and were labeled as R1 and R2. After recording, the resistors were placed in a series to a DC source. Using a multi-tester, the current and voltage drop across each resistor was measured. The multi-tester was adjusted according to the needed unit. The total
current and total voltage across the
combination was also measured. The total resistance was computed using the formula RT = VT/IT, wherein RT = Total Resistance, VT = Total Voltage, and IT = Total Current. Theoretically, the total resistance was computed by adding the values of R1 and R2. The percent error was computed and the 1.63% error may have been from the wrong handling or usage of the multi-tester. Another reason for the percent error is the fact that the measurement of the multi-tester is more accurate compared to the table of values for the color code.
Voltage (V) Current (I)
R1=10X101±5% 9.8 0.0447 A
R2=33X101±5% 9.8 0.0516 A
Theoretical RT= 73.1Ω-80.7Ω
Experimental RT= 77.6Ω
% Error= 0.9%
Table 2. Summary of Data for Parallel Wiring
The second activity for this experiment is almost the same as the first activity in relation to their procedures. However, the two activities only differ in the connection that has been used on each. While the experimenters have used series connection for the resistors in the first activity, the experimenters have used parallel
connection for the resistors in the second activity. The percent error that has been computed in this activity may have been because of the fact that the measurement of
the multi-tester, even though very near, is more accurate compared to the values in the table of values for the color-coding. The formula that have used in this activity to compute for the theoretical value of the resistance is RT = 1/(1/R1)+(1/R2). Electromotive Force of Cell (E) 8V
Known Resistance (R) 100Ω
Current (I) 0.045 A
Internal Resistance of Cell (c) 77.8 Table 3. Summary of Data for Battery Cell The third activity of this experiment involves the usage of a battery cell. This activity is in relation to the 2nd objective of the
experiment, which is to verify the laws on series/parallel resistors and cells. Using a multi-tester and turning it to its voltmeter function, the electromotive force of the cell was determined by connecting the multi-tester directly across the terminals of the battery cell. A known resistance was then connected with the cell. The current delivered to the circuit was measured using an ammeter. With all of the information that has been recorded, the internal resistance of the cell was then computed. The equation used for this activity is r = (E - IR) / I.
5. Conclusion
In this experiment the resistance of a resistor was determined based on its color code. Resistance can be determined in two ways: by standard color code or by voltmeter-ammeter
method. Each resistor has three to four bands present. The color of each band represents a certain value. The first two color band of the resistor is equivalent to a value as a digit. The third color band serves as the multiplier and the last color band is the resistor's tolerance. When these values are combined, the resistance can be known. Voltmeter-ammeter method, on the other hand, makes use of a special device called multimeter that can measure voltages and currents. Whether the circuitry is wired in a series, parallel or series-parallel fashion, voltages and currents can be readily determined by the device. The laws on series/parallel resistors and cells were verified, in a series wiring, currents are equal in every resistor and voltages are not. In a parallel wiring, voltages are equal in every resistor and currents are not.
6. Application
1. The law for series and parallel combination of resistances were verified in the experiment, the results of the group strongly agrees to the relationship of the component of the said circuits which imply to their own different laws. For parallel resistors: the total resistance of a Parallel Circuit is not equal to the sum of the resistors, the total resistance in a parallel circuit is always less than any of the branch resistances and adding more parallel resistances to the paths causes the total resistance in the circuit to decrease. And as for the laws of series resistors, the current flow is the same through each
element of the series circuit, the combined resistance of the various loads in series is the sum of the separate resistances and last, the voltage across the source or power supply is equal to the sum of the voltage drops across the separate loads in series.
2. Series= 20 ohms Parallel= 1.25 ohms
3. The reason the resistance drops to 1000 ohms or less when the skin is wet is because water allows free movement of charges. The water spreads all over our skin, increasing the surface exposure to electricity. The circuit in a lie detector is based on the fact that a person’s skin resistance changes when he sweats (and sweating results from lying). Dry skin has a resistance of about one million ohms, whereas the resistance of moist skin is reduced by a factor of ten or more.
4. An electric circuit is in many ways similar to your circulatory system, in order for a circuit to work the whole circuit has to be connected, just like the circulatory system. The blood vessels, arteries, veins and capillaries of human circulatory system are like the wires in a circuit. The blood vessels carry the flow of blood through your body. The wires in a circuit carry the electric current to various parts of an electrical or electronic system. The heart is the pump that drives the blood circulation in the body and it provides the force or
pressure for blood to circulate and In a circuit the battery pumps the electrons around the circuit so that the bulb is able to work. The blood circulating through the body supplies various organs, like your muscles, brain and digestive system. A battery or generator produces voltage -- the force that drives current through the circuit.
5. The household circuits are generally wired in parallel, which allows you to operate each light or power point independently of the others. This also means the current running through any one section of the parallel circuit stays small enough to prevent problems because in parallel circuits the current is split up and travels along each separate path, if ever they were hooked in series circuit then unplugging one would remove the power to all of them.
6. Ventricular fibrillation is the most common electrical mechanism in cardiac arrest. Defibrillators have various components, including a power source, variable transformer, rectifier, capacitor, switches and paddles. A rectifier, in the capacitor charging circuit, converts AC voltage into DC voltage. DC energy is used rather than AC because it is more effective, causes less myocardial damage and is less arrhythmogenic. A capacitor is the most important part of the defibrillator. A capacitor is formed by a pair of conductors (metal plates) separated by an insulator (a layer of air). A capacitor stores electrical energy in the form of electrical charge. In the capacitor, the
quantity of electrical charge stored for a given charge potential is determined by the surface area of the plates, the thickness of the insulating layer and the ability of the capacitor to store charge (permittivity). During the discharge of a capacitor, delivered energy falls exponentially and some of the energy available is lost in circuit resistance, inductor and paddles. The defibrillator has an inductor in its output circuit. The inductor gives optimum shape and duration to the delivered current.
7. References
Armstrong, T., Starck, J., & LaPlante, R.
(2000). SERIES-PARALLEL
COMBINATION CIRCUITS. Retrieved
April 30, 2015, from
http://www.ibiblio.org/kuphaldt/electricCir cuits/DC/DC_7.html
Chaudhari, M. & Baker, P.(2005). Physical principles of the defibrillator. Elsevier Inc., 6, 12, pp 411–412 DOI: http://dx.doi.org/10.1383/anes.2005.6.12 .411
Soclof, S. (2015) How Circuits Work. Retrieved April 30, 2015, from http://science.howstuffworks.com/enviro nmental/energy/circuit.htm