Lab 217 RC Circuits

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New Jersey Institute Of Technology *

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121A

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Electrical Engineering

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Apr 3, 2024

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Lab 217: RC Circuits Group ID: 6 Date of Experiment: 11/2/2021 Date of Report Submission: 11/9/2021 Phys 121A 001 Instructor: Sandun Amarasinghe 1. Introduction 1.1 Objectives - To observe and analyze the voltage across a capacitor Vc as a function of time t in a circuit containing a resistor and capacitor connected in series. 1.2 Theoretical Background - The objective of this lab is to learn about resistors and capacitors, specifically a RC circuit. We are to gather data on the time it takes for the circuit to charge in one trial and the time it takes to discharge on another. With that data we then measure the time constants.

2. Experimental Procedure Equipment:

Code for finding time constant C = 1000*10^-6; R = 33*1000; V0 = 5; t = 0: 0.01: 200; tau = R*C; Vt = V0*exp(-t/tau); Yth = log(Vt/V0); texp = [0 5.7 11 16 21.3 31.8 42.3 51.9 61]; Vexp = [5 4.5 3.7 3.2 2.9 2.0 1.5 1.0 0.9]; Yexp = log(Vexp/V0); subplot(2,1,1); plot(t, Vt, texp, Vexp, 'x' ); subplot(2,1,2); plot(t, Yth, texp, Yexp, 'x' ); coefficients = polyfit(texp, Yexp,1); m = coefficients (1); tauexp = -1/m; error = abs(tau-tauexp)/tau*100; Code for finding 2 nd time constant C = 1000*10^-6; R = 33*1000; V0 = 5; t = 0: 0.01: 200; tau = R*C; Vt = V0*(1-exp(-t/tau)); Yth = log(1-Vt/V0); texp = [0 4.3 9 14 19.7 29.2 37.7 48.1 59 82]; Vexp = [0 0.68 1.32 1.80 2.1 3 3.5 3.9 4.0 4.6]; Yexp = log(1-Vexp/V0); subplot(2,1,1); plot(t, Vt, texp, Vexp, 'x' ); subplot(2,1,2); plot(t, Yth, texp, Yexp, 'x' ) coefficients = polyfit(texp, Yexp,1); m = coefficients (1); tauexp = -1/m; error = abs(tau-tauexp)/tau*100;

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3. Results and Calculations 3.1 Experimental Data Discharging: Time (s) 0 5.7 11 16 21.3 31.8 42.3 51.9 61 Charge (A) 5 4.5 3.7 3.2 2.9 2.0 1.5 1.0 0.9

Charging: Time (s) 0 4.3 9 14 19.7 29.2 37.7 48.1 59 82 Charge (C) 0 0.68 1.32 1.80 2.1 3 3.5 3.9 4.0 4.6

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4. Discussion and Analysis Part B: Question 10 2. Time it takes for the voltage to decay to half of its maximum. - 0.0028 3. Time it takes for the voltage to decay to one-quarter of its maximum. - 0.0062

4. Time it takes for the voltage to decay to one-eight of its maximum. - 0.0095 5. Theoretical half life q(t) - 0.00325 Question 11 3. Time constant for discharging - -1/225 = 0.004444444 5. Time constant for charging - -1/200 = 0.005 5. Conclusions - In these experiments, we learned how to obtain data on how fast capacitors will charge or discharge to their maximum or minimum potential. We were able to calculate the time constant as well as analyze the half-life. Overall, we gained to understand how voltage works within a capacitor.