Question 714: Current Electricity

Question

In the circuit shown, initially there is no charge on the capacitors and keys S
1
and S
2
are open. The values of the capacitors are C
1
= 10$\mu $F, C
2
= 30$\mu $F and C
3
= C
4
= 80$\mu $F.
Which of the statement(s) is/are correct?
![](https://imagex.cdn.examgoal.net/1ksn79zry/8b278776-a27f-4a2e-80b8-eb8179dfe4ea/5faf97e0-0346-11ec-aa1c-d9fff7d3eb63/file-1ksn79zrz.jpeg)

Accepted Answer

Just after closing of switch charge on any capacitor is zero.
$ 	herefore $ Replace all capacitors by conducting wires.
Current flow in the circuit,
$i = {5 \over {70 + 100 + 30}} = {5 \over {200}} = 25$ mA
Now S
1
is kept closed for long time circuit is in steady state.
${q \over {10}} + {q \over {80}} + {q \over {80}} - 5 = 0 \Rightarrow {{10q} \over {80}} = 5$
$ 	herefore $ $q = 40\mu C$
$ 	herefore $ V across ${C_1} = {{40} \over {10}} = 4V$
Now just after closing S
2
charge on each capacitor remains same.
Applying KVL,
$ - 10 + x 	imes 30 + {{40} \over {10}} + y 	imes 70 = 0$
30x + 70y = 6 .....(1)
$ - {{40} \over {80}} + 5 + (x - y)30 - {{40} \over {80}} + (x + y) 	imes 100 - 10 + x 	imes 30 = 0$
$160x - 130y - 6 = 0$ .... (2)
$y = {{96} \over {1510}}$
x = 0.05 A
![](['https://imagex.cdn.examgoal.net/1ksn7c4r3/6f3d8a9b-073a-4d7e-a25a-cc3b994eb0e2/9b25e9f0-0346-11ec-aa1c-d9fff7d3eb63/file-1ksn7c4r4.jpeg', 'https://imagex.cdn.examgoal.net/1ksn7dbl5/3e6b334d-ebfb-4b74-8fcc-cff15a97c8ae/bc3cd4a0-0346-11ec-aa1c-d9fff7d3eb63/file-1ksn7dbl6.jpeg'])

Answer

The key S
1
is kept closed for long time such that capacitors are fully charged. Now, key S
2
is closed, at this time, the instantaneous current across 30$\Omega $ resistor (between points P and Q) will be 0.2 A (round off to 1
st
decimal place).

Answer

If key S
1
is kept closed for long time such that capacitors are fully charged, the voltage across the capacitor C
1
will be 4V.

Answer

At time t = 0, the key S
1
is closed, the instantaneous current in the closed circuit will be 25 mA.

Answer

If key S
1
is kept closed for long time such that the capacitors are fully charged, the voltage difference between points P and Q will be 10 V.

Current Electricity

In the circuit shown, initially there is no charge on the capacitors and keys S 1 and S 2 are open. The values of the capacitors are C 1 = 10\mu F, C 2 = 30\mu F and C 3 = C 4 = 80\mu F. Which of the statement(s) is/are correct?

Choose the correct answer: