Question:

In the circuit shown, initially there is no charge on capacitors and keys S1 and S2 are open. The values of the capacitors are C1=10µF, C2=30µF, and C3=C4=80µF. Which statements is/are correct?

If key S1 is kept closed for a long time such that capacitors are fully charged, the voltage across C1 will be 4V.

The key S1 is kept closed for a long time such that capacitors are fully charged. Now key S2 is closed, at this time the instantaneous current across 3Ω resistor (between points P Q) will be 0.2A (round off to 1st decimal place.

At time t=0, the key S1 is closed, the instantaneous current in the closed circuit will be 25mA

If S1 is kept closed for a long time such that capacitors are fully charged, the voltage difference between P and Q will be 10V

Solution:

Correct option is C. At time t=0, the key S1 is closed, the instantaneous current in the closed circuit will be 25mA. Just after closing of switch S1, charge on capacitors is zero. Therefore, replace all capacitors with wire. i = 5/200 = 25mA. Now S1 is kept closed for a long time; the circuit is in a steady state. q10 + q80 + q80 - 5 = 0 10q80 = 5 Therefore, q = 40µC Therefore, V across C1 = 40/10 = 4 volt. Now just after closing of S2, charge on each capacitor remains the same. KVL -10 + x × 30 + 40/10 + y × 30 = 0 x + 70y = 6 (1) -40/80 + 5 + (x - y)30 - 40/80 + (x - y) × 100 - 10 + x × 30 = 0 160x - 130y - 6 = 0 (2) y = 96/15 10x = 0.5 amp. Correct option = 2, 3.