Question 87: Current Electricity

Question

In the circuit shown, initially there is no charge on the capacitors and keys S1 and S2 are open. The values of the capacitors are C1 = 10$$\mu $$F, C2 = 30$$\mu $$F and C3 = C4 = 80$$\mu $$F.  Which of the statement(s) is/are correct?

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

Answer

The key S1 is kept closed for long time such that capacitors are fully charged. Now, key S2 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 1st decimal place).

Answer

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

Answer

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

Answer

If key S1 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 S1 and S2 are open. The values of the capacitors are C1 = 10$\mu F, C2 = 30\mu F and C3 = C4 = 80\mu $F. Which of the statement(s) is/are correct?

Choose the correct answer: