Capacitor Charging / Discharging

In this lab we observed the relations of charging and discharging a capacitor. The relation we see from our equations is that it will essentially never fully charge or discharge as it exponentially approaches either value. With the given knowledge of capacitors we are to construct a circuit from which we determine the thevin values.

We utilize a 9 V DC power supply and determine that C = 62uF from w = CV^2 / 2. There is a charging interval of about 20s with a resulting stored energy of 2.5 mJ and then discharged in 2 s.

Assuming an ideal capacitance we estimate charging resistance to be 64.5 k ohms

Using V = IR we determine the peak current value to be 0.14 mA and P = IV to determine peak power to be 1.26 mW.

The discharging resistance is estimated to be 6.45 k ohms and the peak discharge current and power are 1.4 mA and 12.6 mW respectively.

We set the power sipply to be 6 V         V measured = 5.707 V

VFinal = Vs (RLeak)/(Rc + RLeak)         RLeak = 1.256 M ohms

Graph of charging capacitor 

 charging took about 20 seconds

Graph of discharging capacito

discharging took about 2 seconds

Questions:

1. Thevenin Values During Charging

RTH = 61.4 k ohms

VTH = 5.707 V

2. Thevenin Values During Disharging

RTH = 6.42 k ohms

VTH = 5.707 V

3. 0.3679 * VF = 3.607 V  this occurs around 4s according to our charging waveform

t=RC    4 = R * 62 uF   R = 64.5 K ohms

Practical Question:

1. E = V^2 C/2 = 160 mJ = 15kV^2  C / 2       C = 1.4 F

2. C||C + C||C + C||C + C||C = 1.4 F

C = .7