Lab 6 (1)

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Capitol Technology University *

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Electrical Engineering

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Apr 3, 2024

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Capacitors Lab 6 EL-100 Work done: 11/1/18 Date of Submission: 11/21/18 Christian Michael Allen Feldmann Purpose: In this lab, we built different circuits to measure capacitance in a circuit through different layouts.

Equipment and Materials: For this lab, we used the XK-150 digital trainer, the BK Test Bench 388A digital multimeter (DMM), various pieces of wire, three resistors with resistances of 2.7kΩ, 3.9kΩ, and 10kΩ, and three capacitors with capacitances of 2.2µF, .47µF, and .33µF. Procedure: First, we used the DMM to measure the actual capacitance of each capacitor and the resistance of each resistor, and compared those values to the theoretical values. We then set the voltage to approximately 18 volts. Next, we used the three capacitors and a few wires to built the circuit shown in Fig 1a and measured the total capacitance in Table 4a. We also calculated the total capacitance using the theoretical values of the capacitors, and calculated the percent error between these two values. We then repeated this for Figs 1b, 1c, and 1d. Fig 1a

Fig 1b Fig 1c

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Fig 1d Next, we used the three capacitors, the three resistors, and various wires to create the circuit shown in Fig 2. We then measured the voltage across each capacitor in the circuit. We also calculated the voltage drop across each capacitor using the theoretical values. Fig 2 Then, we rebuilt the circuit shown in Fig 1b and measured the voltage across each capacitor. We also calculated the voltage drop using the theoretical values. Last, we repeated this for Fig 1c.

Data: Nominal Measured C 1 2.2µF 2.301µF C 2 .47µF .41µF C 3 .33µF .324µF Table 2 Expected and measured capacitance Nominal Measured R 1 2.7kΩ 2.66kΩ R 2 3.9kΩ 3.87kΩ R 3 10kΩ 10.03kΩ Table 3 Expected and measured resistance Circuit Measured Fig 1a 3.04µF Fig 1b .168µF Fig 1c .553µF Fig 1d .292µF Table 4a Measured total capacitances of various circuits Measured V 1 2.89V V 2 4.2V V 3 10.89V Table 5a Measured voltage drops in Fig 2 Fig 1b Fig 1c

V 1 1.66V 5.58V V 2 6.83V 11.83V V 3 9.72V 12.08V Table 6a Measured voltages drops in Fig 1b and Fig 1c Calculations: Circuit Calculated % Difference Fig 1a 3µF 1.32% Fig 1b .18µF 6.67% Fig 1c .59µF 6.27% Fig 1d .29µF 0.69% Table 4b Calculated total capacitance of various circuits Circuit Equation Fig 1a C T = C 1 + C 2 + C 3 = 2.2µF + .47µF + .33µF = 3µF Fig 1b C T = 1/((1/C 1 ) + (1/C 2 ) + (1/C 3 )) = 1/((1/2.2µF) + (1/.47µF) + (1/.33µF)) = .18µF Fig 1c C T = (C 1 * (C 2 + C 3 )) / (C 1 + (C 2 + C 3 )) = (2.2µF * (.47µF + .33µF)) / (2.2µF + (.47µF + .33µF)) = .59µF Fig 1d C T = ((C 1 + C 2 ) * C 3 ) / ((C 1 + C 2 ) + C 3 ) = ((2.2µF + .47µF) * .33µF) / ((2.2µF + .47µF) + .33µF) = .29µF Table 4c Equations used in Table 4b Calculated V 1 2.93V V 2 4.23V V 3 10.84V Table 5b Calculated voltage drops in Fig 2 Equation V 1 V 1 = (R 1 / R T ) * E = (2.7kΩ / 16.6kΩ) * 18V = 2.93V

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V 2 V 2 = (R 2 / R T ) * E = (3.9kΩ / 16.6kΩ) * 18V = 4.23V V 3 V 3 = (R 3 / R T ) * E = (10kΩ / 16.6kΩ) * 18V = 10.84V Table 5c Equations used in Table 5b Fig 1b % Difference Fig 1c % Difference V 1 1.47V -11.45% 4.83V -13.44% V 2 6.89V .88% 13.28V 12.26% V 3 9.82V 1.03% 13.28V 9.93% Table 6b Calculated voltage drops in Fig 1b and Fig 1c with % difference between values in Table 6a and Table 6b Fig 1b Equation Fig 1c Equation V 1 V 1 = (C T / C 1 ) * E = (.18µF / 2.2µF) * 18V = 1.47V V 1 = (C T / C 1 ) * E = (.59µF / 2.2µF) * 18V = 4.83V V 2 V 2 = (C T / C 2 ) * E = (.18µF / .47µF) * 18V = 6.89V V 2 = (C T / C 23 ) * E = (.59µF / .8µF) * 18V = 13.28V V 3 V 3 = (C T / C 3 ) * E = (.18µF / .33µF) * 18V = 9.82V V 3 = (C T / C 23 ) * E = (.59µF / .8µF) * 18V = 13.28V Table 6c Equations used to calculate values in Table 6b Conclusion: A: Questions Q1) For Figure 1b, compute the voltage across each capacitor and record in Table 6b. Repeat for Figure 1c. A1) See Table 6b in Calculations. Q2) Measure and record the voltages across each capacitor for the above figures. Include the % difference between Tables 6a and 6b. A2) See Table 6a in Data. B: Personal Conclusions The work done and the circuits built served well as an introduction to capacitors and how to measure voltage across them. It was a tad bit difficult to get the exact voltage at full charge, as they were a bit finicky when attempting to keep them at maximum charge, but overall the lab served its purpose well. C: Contributions Allen Feldmann: Purpose, Equipment and Materials, Data, Calculations.

Christian Michael: Procedure, Conclusion.