Lab 11: Capacitor Charging/Discharging

Intro:

The purpose of this lab was to observe the charging and discharging of a capacitor.  We built a circuit with a 9V DC power supply that charges 2.5mj for 20s, and discharges in 2s. The time it takes for a capacitor to charge up is 5τ. Where τ = RC. We will model a real storage capacitor with the figure below and find the Thevenin equivalent.

Data:

W=2.5mj         t= 20s              Vs=9

Vcap = Vs(1-e^(5t/τ) = 9.939

C= 2*W/Vcap^2 = 62.57μF

Charging:

20=Rc*C à Rc=64800Ω

I= Vs/Rc= 0.139mA

P=IV=1.25W

V_final= 8.87

V_final = R_leak / Rc + R_leak à R_leak = 4421353Ω

Charging Process

Discharging:

2=Rd*C à Rd=639.2Ω

I= Vs/Rc= 1.93mA

P=IV=.0125W

Discharging Process

Analysis:

During charging the thevein resistance is found with Vth = R_leak * Rc / (Rc + R_leak) = 63017Ω. During discharging the thevein resistance is 639.1Ω. Vth = Vcap = 9.939V