# Calculating forced response in RC circuit

In one my assignment questions, I need to find voltage across a capacitor. This is the diagram given:

And the conditions given are:

1- Switches A and B are in perfect sync, and when A opens, B closes and vice versa. Also their positions change every 30 ms.

2- Initially switch A is open. Assume steady state is achieved

And the question is to find voltage across capacitor at time instances:

1. t=0+ and 0-
2. t=50ms+ and 50ms-
3. 60 ms

So considering the open switch and steady state condition of capacitor (acts as open circuit). I reduced the circuit to this:

The voltage across capacitor will be same as voltage across the 7 ohm resistor.

Applying current division and also taking into consideration the 3A current through the 7 ohm resistor, I got voltage across the resistor as approx 23.205 Volts.

Also as this is a forced response, the voltage across capacitor will be Vc = Vo - Voe^(-t/RC)

So at t=0+ and 0-, i.e steady state Vc = Vo = 23.205 volts.

But I am unable solve for the other parts i.e 50ms and 60ms as I am not sure how to take into account the position change in both the switches. How do I go about it ?

• think about this ... when does the current from the 10 A source flow on the left side of switch A? Mar 12, 2021 at 7:28
• +1 for identifying this as an assignment and showing some work. Mar 12, 2021 at 15:03