Series, Parallel and Series/Parallel Resistive Circuit Andrea Allen L. Lu Malayan Colleges Laguna
[email protected]
ABSTRACT Different circuit flow corresponds to different current, resistance and voltage being experienced by each component. component. In series circuit, circuit, currents currents are equal with one another and both voltage and resistance are additive. In parallel circuit, voltages are equal with one another, additive current and inversely additive resistance. In series/parallel circuit, arranging the circuit network first to either series or parallel enables in computing the three variables. DC fundamentals circuit boards and multimeter is used in conducting the experiment.
KEYWORDS Series, Parallel, Series-Parallel, Current, Voltage, Resistance, Ohm’s Law
1 INTRODUCTION
The total resistance is found by simply adding all the resistance of each resistor as depicted in Eqn (2) (2) = + 2 + ⋯ + The total voltage of each resistor is also found by simply adding them all as depicted depicted in Eqn (3) (3) = + 2 + ⋯ + Parallel circuits consist of two separate independent circuits where once a current flowed through it the current can choose where will it flow (Osbourne, 2018). The total current now is the additive of all current flowing through each resistor as shown in Eqn (4) (4) = + 2 + ⋯ + The total resistance is the additive inverse of all resistor present in the circuit as shown in Eqn (5) 1
There are different types of circuit, namely, series, parallel or the combination of the two. Different types of circuits have their own corresponding current, resistance and voltage being experienced by the components in the circuit. According to Campbell et al. (2018), in a series circuit provides only one path for the electric current to flow. Each component is dependent from one another, thus, if one component is removed, the other component will automatically shut down. This type of circuit is usually used in circuit breakers and fuses for safety purposes. The current current is equal all through each resistor as depicted in Eqn (1): (1) = = 2 =
1
=
1 +
2
1 + ⋯+
(5)
The total voltage supplied by the voltage source is the same all throughout the circuit as shown in Eqn (6) = = 2 =
6
In a series-parallel circuit, the rules for both series and parallel are not applicable. The circuit diagram should be arranged first in either in a series or parallel in order to compute the current, resistance and voltage present in the circuit flow.
2 RESULTS
Table 1 summarized the results obtained in measuring and calculating the resistance of a series circuit. When CM switch 1 is on the measured R1 was different from the original resistance. This phenomenon also happened in R2 when CM switch 2 is on. The CM switches lowers the resistance of the resistor corresponding to the number of switch that was on. Table 1. Resistance in a Series Resistive Circuit
Description Results Measure: R1 991 Ω R2 1184 Ω R3 612 Ω R T 2788 Ω Measure Resistance with CM switch 1 on: R1 498 Ω R2 1184 Ω R3 612 Ω R T 2294 Ω (1) Resistor that R1 only by 493 Ω changed and its value (2) R T 2294 Ω Measure Resistance with CM switch 2 on: R1 991 Ω R2 1184 Ω R3 1234 Ω R T 3409 Ω Compare measured R2 changed by 622 Ω value with measured value of CM switch 1 on The calculated current using Ohm’s Law and the measured current using the multimeter were almost the same proving that the current in a series circuit are equal with one another as shown in table 2.
Table 2. Current in a Series Resistive Circuit
Description Source Voltage Resistance from resistor color code Circuit current using Ohm’s Law Resistance when two-post connector is removed Current when two post connector is replaced by test leads R T when CM switch 1 is on Calculated IT using R T when CM switch 1 is on Measured IT when CM switch 1 is on R T when CM switch 2 is on IT when CM switch 2 is on Comparison of R T and IT when CM switch 2 is on
Results 15.04 V 2820 Ω 5.333 mA 2789 Ω
5.37 mA
2300 Ω 6.5391 mA
6.57 mA 3402 Ω 4.4209 mA R T increased IT decreased
The calculated total voltages across each resistor was the same as the voltage source measured. This proved the rule in series circuit that adding all the voltages across each resistor is equal to the total voltage source. Table 3. Voltage in a Series Resistive Circuit
Description Results VA and IT when 15.02 V two-post is connected, 5.40 mA respectively Voltage drop using Ohm’s Law: V1 5.3352 V V2 6.3936 V V3 3.3048 V
Measured Voltage drop : V1 V2 V3
5.34 V 6.38 V 3.301 V
Table 4 showed that the measured equivalent resistance is equal the calculated equivalent resistance using Eqn (5) as mentioned before. Table 4. Resistance in a Parallel Resistive Circuit
Description Measure: R1 R2 R3 R E Calculate: R E
Results 9970 2176 4620 1288
Ω
1.51 mA 6.83 mA 8.33 mA 1784 Ω 1.49 mA 6.94 mA 8.45 mA
In table 6, it could be observed that there was a little discrepancy with the measured and calculated resistance. This was due to possible human error in computing the resistance in a combination circuit.
Ω
Table 6. Resistance in Series/Parallel Resistive Circuit
Ω Ω
1288.15
Ω
The measured voltages across each resistor was the same as the voltage source (VA). Also adding all the current flowing in each resistor gave the total current which was the same as the calculated total current. It was also observed that adding resistance increases the total current in the circuit. Table 5. Voltage and Current in a Parallel Resistive Circuit
Description Measure: VA VR1 VR2 VR3 Calculate: IR1 IT Measure: IR1 IT Add: R2 Calculate: R E
IR1 IR2 IT Measure: R E IR1 IR2 IT
Results 15.02 V 15.02 V 15.02 V 15.02 V 1.51 mA 1.51 mA 1.49 mA 1.49 mA 2200 1802.3
Ω Ω
Description Calculated: R E R T Measure: R E R T
Result 800 Ω 1130 Ω 790 Ω 1120 Ω
There was a very little discrepancy between the measured and calculated voltage value that it be considered negligible. Table 7. Voltage in Series/Parallel Resistive Circuit
Description Calculated: R T IT VRE VR1 Measured: VRE VR1
Result
1130 Ω 0.0133 A 10.62 V 4.38 V 10.71 V 4.37 V
Same thing happened in the calculation and measurement of current in a series-parallel circuit. There was a little bit discrepancy but it could be neglected since it was within the tolerance.
Table 8. Current in Series/Parallel Resistive Circuit
Description Calculated: IT VR1 VRE IR2 IR3 IT IR2 + IR3 = IT Measured: IT IR2 IR3 IR2 Within tolerance
Result 13.27 mA 4.38 V 10.62 V 8.85 mA 4.42 mA 13.27 mA Yes 13.55 mA 9.09 mA 4.53 mA 0.80 mA Yes
6 CONCLUSIONS
In conclusion, the rules of series and parallel circuits were all true and correct and has been proven by the experiments conducted. Current flowing in a series connection were equal with one another. Addition of all resistance and voltage present in the circuit gave the total resistance and total voltage. Also, it was observed that resistance is inversely proportional with current. The higher the current flowing the lower the total resistance will be. However, the effect of current to voltage drop is the complete opposite of the effect in resistance. Voltage drop is directly proportional with current. The higher the current flowing the higher the voltage drop a circuit is experiencing. In parallel circuit, instead of having same current it was the voltage that have the same reading. Total resistance was the addition of inverse of resistor’s each resistance while the current is the addition of all current flowing in the resistor. Current increases if addition of resistance happens.
REFERENCES Campbell, A., Hanania, J. & Donev, J. (2018). Series circuit. Retrived from https://energyeducation.ca/encyclopedia/Series_circui t Osbourne, J. (2018). Resistors in parallel. Retrieved from https://www.brightstorm.com/science/physics/electric ity/resistors-in-parallel/
