Lab 7 Capacitors

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St. Petersburg College *

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1054

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Electrical Engineering

Date

Dec 6, 2023

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pdf

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1 Lab 7: Capacitors Objective: The purpose of this lab is to study circuits with capacitors using simulated electric circuits. Procedure: 1. You do not need to write a full lab report for this lab. Record the Title, date, and page numbers in your lab report. Then follow the steps below. Copy each question, and then add the answer below the question. Be sure to clearly label all data that you record into your lab report. Be sure to write down all equations used and show all calculations completely. 2. Review capacitors section in Chapter 19 and 21 in your textbook and PPT slides. 3. First, we are going to find theoretical values using the circuits shown below. Copy the circuits to your lab report, and answer the questions. Part A: Capacitors in Series 4. Three capacitors (C1 = 1 x 10 -13 F, C2 = 2 x 10 -13 F and C3 = 3 x 10 -13 F) are connected in series as shown in Figure 1. The battery voltage is 1.5 V. Internal resistance of the battery and wire resistance are negligible. Figure 1 5. Calculate the following values. Show complete work. A) Calculate the equivalent capacitance of the circuit. Equivalence Capacitance. 1/C = 1/C1 + 1/C2 + 1/C3 1/C= 10^13 (1/1 +1/2+1/3) C= 6/11 x 10^-13 C= 0.545 x 10^-13 F  answer

2 B) Calculate the total charge Q stored in the three capacitors (this is the same charge in a capacitor with the equivalent capacitance calculated above). Q = C(eq) V = 0.545 x 1.5 x 10^-13 C → Q = 0.818 x 10^-13 C C) Calculate the voltage across C1, voltage across C2, and voltage across C3. Q/C = V V (c1) = Q/ C1 = 0.818 x 10^-13/ 1 x 10^-13 → Vc1 = 0.818 V V (c2) = 0.818 x 10^-13 / 2 x 10^-13 → Vc2 = 0.409 V V (c3) = 0.818 x 10^-13 / 3 x 10^-13 → Vc3 = 0.273 V D) Do above voltage values add up to the voltage provided by the battery? Yes, the above voltage values add up to the voltage provided because if you add them up, it will equal to 1.5 V. Values calculated in steps A-D are theoretical values for capacitors in series. Now, we build the same circuit using a PhET simulation. Part B: Capacitors in Parallel 6. Three capacitors (C1 = 1 x 10 -13 F, C2 = 2 x 10 -13 F and C3 = 3 x 10 -13 F) are connected in parallel as shown in Figure 2. The battery voltage is 1.5 V. Internal resistance of the battery and wire resistance are negligible. Figure 2

3 7. Calculate the following values. Show complete work. E) Calculate the equivalent capacitance of the circuit. C(eq) = C1 + C2 + C3 = (1+2+3) x 10^-13 F → C(eq) = 6 x 10^-13 F F) Calculate the total charge Q stored in the three capacitors (this is the same charge in a capacitor with the equivalent capacitance calculated above). Q = C(eq) V = (6 x 10^-13 F) (1.5V) → Q= 9 x 10^-13 C G) Calculate the charge in C1, charge in C2, and charge in C3. Charge for C1 Q1= C1V0 = (1 x 10^-13F)(1.5V) → Q1 = 1.5 x 10^-13 C Charge for C2 Q2 = C2V0 = (2 x 10^-13)(1.5V) → Q2 = 3 x 10^-13C Charge for C3 Q3= C3V0 = (3 x 10^-13F)(1.5V) → Q3 = 4.5 x 10^-13C H) Do above charge values in step (G) values add up to the total charge calculated in step (F)? The sum would be Q 1 +2 +3 (1.5 x 10^-13) + (3x 10^-13) + (4.5 x 10^-13)

4 → 9 x 10^-13 C Values calculated in steps E-G are theoretical values for capacitors in parallel. Part C: Capacitors in both Series & Parallel 8. Three capacitors (C1 = 1 x 10 -13 F, C2 = 2 x 10 -13 F and C3 = 3 x 10 -13 F) are connected as shown in Figure 3. The battery voltage is 1.5 V. Internal resistance of the battery and wire resistance are negligible. Figure 3 9. Calculate the equivalent capacitance of the circuit. Show complete work. This is the theoretical value for the capacitor combination. Simulated Values: 10. Now we are going to build the circuits shown in Figure 1, Figure 2 and Figure 3 using a PhET simulation. Go to PhET simulation https://phet.colorado.edu/sims/cheerpj/capacitor-lab/latest/capacitor- lab.html?simulation=capacitor-lab 11. Spend a few minutes exploring the functionalities of the different tabs/panels. 12. Go to Multiple Capacitors tab. Check “ Plate Charges ”, “Total Capacitance”, “Stored Charge”, and “Voltmeter” boxes. 13. Build the circuit shown in Figure 1 (capacitors in series) by using “3 in Series” option . Change capacitance values according to C1, C2 and C3 values given in step 4, and set

5 battery voltage to 1.5 V. Complete Table 1 using the values shown in the simulation. Use the Voltmeter in the simulation to measure voltage across each capacitor. 14. Take a screenshot of the circuit and copy it to your lab report. Capacitors in Series photo 1,2,3 C1

6 C2

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