Solving Transient Analysis RC: Find Capacitance for 200V, 20V, 2V

[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

Homework Equations

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

ic = c v'

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

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.




Your help is much appreciated!

 

[gneill]

Suppose that the second switch didn't open at time 100μs. What would be the eventual voltage across the capacitor after the proverbial "long time"?

That should tell you what the function is that describes the voltage up until the instant that that second switch opens.