# Transient Analysis RC

1. Nov 29, 2011

### tdabboud

1. The problem statement:

What is the value of capacitance needed in Fig. 1 so that the voltage across the capacitor never exceeds (a) 200 V, (b) 20 V, and (c) 2 V ?

This is the Circuit

2. Relevant equations

Vc(0-) = 0V
Vc(0+) = 150V

ic = c v'

vc(t) = final + [initial - final] e^(-t/τau)

3. The attempt at a solution
since the capacitor is in parallel with the resistor the voltages are equal. which at t=0 will be 150V. up until 100us the capacitor is charging, then when t>100us the capacitor will discharge. so the max voltage across the capacitor will be 150V no matter what the value is. However you can get a smaller capacitance value to decrease this voltage but the voltage will never exceed 150V.

I broke the problem into two transient problems:
(1) t=0+ and t=100us-
(2) t=100us+ and t=infinity-

I tried to solve for Vc(t) for each of these problems:

for (1) Vc(t) = 20 - 20e^(-t/c)
for (2) Vc(t) = 20e^(-t/2c)

This did not work out right. So then I tried converting to non ideal current source, but got stuck.

4.PROBLEM
- I have never done a transient problem where the switch changes at some value other then 0.
-I simulated this circuit on pspice and I get the capacitance for each voltage, BUT I want to know how to do this by hand.