Lab 5 - Series&Parallel DC Circuits PDF

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Series & Parallel DC Circuits Electrical Circuits, Eng Gen 220

April 27, 2019

Name: Davion Brown Partner: Jesse Ramirez

Objective The purpose of this lab is to use simple series-only and parallel-only sub-circuit techniques to solve for desired voltages and currents. The application of voltage divider and current divider rules along with Kirchoff’s Voltage (KVL) and Current Laws (KCL) will be used to analyze each sub-network. Two separate combination circuits using resistors (in series and parallel) and a DC voltage source will be constructed and used to help identify if these predictions hold true in actual experiments.

Conclusion All DC Circuit analysis (determining of currents, voltages and resistances within a circuit) can be done with the use of the rules involving Ohm’s Law, KVL and KCL. These are three of the most basic techniques for the analysis of linear circuits. The purpose of this lab was to prove these three laws are valid with two separate series-parallel combination circuits. Prior to building both circuits, the values for the voltages and currents throughout each circuit was found using voltage/current divider.

In circuit one, the measured values for voltages at points (A, B, and C) were (10, 6.02 and 6.02)Volts, respectively. Also, the measured currents flowing through resistors (R1, R2, and R3) were (4.02, 2.73 and 1.29)mA. In circuit two, the measured values for voltages at points (B, C, D and E) were (20, 20, 16.8 and 9.9)Volts. Additionally, the measured currents flowing through (source, R1 and R2) were (22.2, 20.7 and 1.47)mA. The discrepancies between the measured and expected values were nearly non-existent, thus all three of the laws should be considered valid.

Discussion To investigate the first part of the lab, a series-parallel DC circuit was simulated to involve three resistors R1(1k), R2(2.2k), R3(4.7k) and a 10 Volt power source. R2 is in parallel with R3, and that combination is in series with R1. Based on that observation, the theoretical voltages at points A, B, and C with respect to ground are (10, 6, and 6)Volts, respectively. After constructing the circuit and setting the Digital Multi-meter (DMM) to read DC voltage, the measured voltages turned out to be (10, 6.02, and 6.02)Volts, respectively. The deviations between the tested and measured values were determined to be smaller than 1%.

Applying KCL to the parallel sub-network, the current entering node B(i.e., the current though R1(4 ma)] should equal the sum of the currents flowing through R2(2.73ma) and R3(1.28mA). These currents may be determined through Ohm’s Law and/or the Current Divider Rule. Using the DMM as an ammeter, the three currents were measured to be (4.02, 2.73, and 1.29)mA, respectively. The deviations between the measured and calculated current values were within less than 1%.

To investigate the second part of the lab, a series-parallel DC circuit was simulated to involve four resistors R1(1k), R2(2.2k), R3(4.7k) , R4(6.8k) and a 20 Volt power source. R2, R3 and R4 create a series sub-network. That sub-network was in parallel with R1. By observation the voltages at nodes A, B and C were identical (20 volts) as any parallel circuit of similar construction. Due to the series connection, the same current flows through R2, R3, and R4. Furthermore, the voltages across R2(3.21V), R3(6.86V), and R4(9.93V) sums up to the voltage at node C(20.0V). Finally, the current leaving the source(21.5mA) must equal the sum of the currents entering R1(20.0mA) and R2(1.46mA).

After constructing Circuit two with resistors R1, R2, R3, R4 and a power source of 20 volts, the voltages at point B, C, D and E were calculated to be (20, 20, 16.8 and 9.90)V, respectively. These potentials were measured using the DMM. The deviations between the measured and calculated values for voltages were (0, 0, 0.119, and -0.303)%. The measured currents leaving the source(22.2mA) and flowing through R1(20.7mA) and R2(1.47mA) were found using the

DMM as an ammeter. The deviations between the measured and calculated values for currents were (3.33, 3.38, 0.68)%.

Data

Voltage V_A V_B V_C Current R1 R2 R3

Voltage V_B V_C V_D V_E Current Source R1 R2

Circuit One: Theory(V) Measured(V) 10 10 6 6.02 6 6.02 Theory(mA) 4 2.73 1.28

Measured(mA) 4.02 2.73 1.29

Circuit Two: Theory(V) Measured(V) 20 20 20 20 16.78 16.8 9.93 9.9 Theory(mA) 21.5 20 1.46

Measured(mA) 22.2 20.7 1.47

Deviation 0 0.33 0.33 Deviation 0.498 0 0.775

Deviation 0 0 0.119 -0.303 Deviation 3.33 3.38 0.68

Answers to questions 1. Are KVL and KCL satisfied in Tables 1 and 2? Why? Yes. KVL and KCL is satisfied in Table 1 and 2, because the algebraic sum of voltages in the loop of the simplified version of the first circuit is equal to zero. Also, the algebraic sum of currents at node B is equal to zero. Circuit 1: KVL → 10V – 4.0023m(1K) – 4.0023m(1.49855K) = 0 Circuit 1: KCL

→

4.02mA – 2.73mA – 1.29mA = 0

2. Are KVL and KCL satisfied in Tables 3 and 4? Why? Yes. KVL and KCL is satisfied in Table 3 and 4, because the algebraic sum of voltages in the loop of the simplified version of the first circuit is equal to zero. Also, the algebraic sum of currents at node B is equal to zero. Circuit 1: KVL → 20V – 21.459m(0.93197K) = 0 Circuit 1: KCL

→

21.46m – 20.0m – 1.46m = 0

3. How would the voltages at A and B in Figure 1 change if a fourth resistor equal to 10k was added in parallel with R3? What if this resistor was added in series with R3? If a fourth resistor(10K) was added in parallel with R3, the voltages at A and B would be (20 and 11.3)V, respectively. If a fourth resistor(10K) was added in series with R3, the voltages at A and B would be (20 and 6.86)V, respectively.

4. How would the currents through R1 and R2 in Figure 2 change if a fifth resistor equal to 10k was added in series with R1? What if this resistor was added in parallel with R1? If a fifth resistor(10K) was added in series with R1, the currents at R1 and R2 would be (1.82 and 1.46)mA, respectively....