DC Simulation Summary

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Indiana University, Purdue University, Indianapolis *

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Electrical Engineering

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Apr 3, 2024

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DC Circuits Using PhET Simulator Faith Bittner The DC circuit simulation was an experiment that demonstrated Kirchoff’s Rules. The Current Law states that “the total current directed into a junction must equal the total current directed out of the junction” (Sengupta). This is because the current coming into a junction has no other place to go other than out to conserve the charge. This rule is applied to circuits in parallel. The Law of Voltage states that “the sum of the potential drops equals the sum of the potential rises” to conserve energy (Sengupta). This law is useful for circuits in series. For the first activity, a DC circuit was designed at my own discretion. Two loops, three different resistors, and two different batteries were required. The resistors and batteries also had to be on different legs, meaning that each leg had only one resistor. Two legs contained both a battery and a resistor. The values for each battery and resistor were also free range. The resulting circuit is pictured in Figure 1. Figure 1. Hand Drawn Circuit

Then, Kirchoff’s equations were applied to the circuit. Based on the prior statement of Kirchoff’s Laws, the current flowing through the right-hand node must equal the current that flows out of it. Also, each loop must have a total voltage drop of zero. Therefore, three equations can be set up for this specific circuit. In addition, Ohm’s Law was utilized. I 2 = I 1 + I 3 (1) V B1 – V R1 – V R2 = 0 (2) V B2 – V R3 – V R2 = 0 (3) V=IR (4) Using algebraic rearrangement and substitution, the three unknown currents were solved for. The full calculations for the three currents are shown in Figure 2. Figure 2. Calculations for Each Current.

Equation 4 was used to determine the voltage drop across each resistor. It’s important to note that each resistor experiences a voltage drop from the original voltage of each appropriate battery. So, while each voltage drop mathematically comes out as a positive number, it represents the amount of voltage that is lost through each resistor. Thus, the voltage drop across each resistor can be signified either as a negative voltage or a loss of a positive voltage. As for the polarity of the voltage drops, the positive end of the resistor is where the current enters and vice versa for the negative end. This is also shown in Figure 1. The calculations for the voltage drops are represented in Figure 3. Figure 3. Voltage Drop Across Each Resistor Again, these values are positive, but they signify the amount of voltage that is lost from the original battery. For example, the voltage drop across resistor 1 is 5.7 V, so the original voltage of 10 (from battery 1) loses 5.7 volts through resistor 1. Finally, the calculated values were substituted into Equations 2 and 3 to confirm the calculations. The calculations for this are shown in Figure 4. Figure 4. Confirmation of Voltage Drops. As seen above, the sum of the voltages does not equal exactly zero. However, this can simply be attributed to rounding of values. The current values in Figure 2 were rounded off, which means that each voltage drop is rounded off also. This explains why the sum of the voltages is 0.04

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instead of zero. If the unrounded values were used, zero would have been the resulting answer. These values should have been used, instead of rounding, to fully understand Kirchoff’s Voltage Law. Activity 2 was using a simulation to confirm the calculations from Activity 1. The simulator tools were used to replicate the hand drawn simulation, and the result is displayed in Figure 5. Figure 5. Simulation of Hand-drawn Circuit . Using the Ammeter on each leg resulted in the same currents that were calculated in Activity 1. Thus, proving that Kirchoff’s Current Law was upheld. This is shown in Figures 6, 7, and 8.

Figure 6. Current 1. Figure 7. Current 2.

Figure 8. Current 3. Similarly, the voltmeter was used to verify the calculated voltage drops across each resistor. Again, the values matched, so Kirchoff’s Voltage law was proven to be correct for the circuit. This is demonstrated in Figures 9, 10, and 11. Any variation from the calculated voltage drops is, again, due to rounding. Figure 9. Voltage Drop Across Resistor 1.

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Figure 10. Voltage Drop Across Resistor 2. Figure 11. Voltage Drop Across Resistor 3.

References 1. Dr. Aparajita Sengupta. Lecture 8 Notes. 2. PhET Simulator for DC Circuits https://phet.colorado.edu/sims/html/circuit-construction- kit-dc/latest/circuit-construction-kit-dc_en.html 3. PHYS-P 202: DC Circuits Using PhET Simulator Lab Manual 2024