In the circuit shown, initially there is no charge on capacitors and keys $S_{1}$ and $S_{2}$ are open. The values of the capacitors are $C_{1} = 10 μ F$ , $C_{2} = 30 μ F$ and $C_{3} = C_{4} = 80 μ F$ .

Which of the statement(s) is/are correct [2019]

Question

In the circuit shown, initially there is no charge on capacitors and keys $S_{1}$ and $S_{2}$ are open. The values of the capacitors are $C_{1} = 10 μ F$ , $C_{2} = 30 μ F$ and $C_{3} = C_{4} = 80 μ F$ .

Which of the statement(s) is/are correct [2019]

Which of the statement(s) is/are correct? [2019]

Smart Achievers · Accepted Answer

(3, 4)

$+ S_{1}$ closed and $S_{2}$ open, then at $t = 0$ , charge on each capacitor is zero.

$∴$ $I = \frac{V}{R} = \frac{5}{70 + 100 + 30} = 0.025 A = 25 mA$

When switch $S_{1}$ is closed for a long time, all the capacitors are fully charged. As the capacitors are in series, these carry equal charge $q$ .

Current in the circuit is now zero as the circuit is in steady state.

Applying Kirchhoff's voltage law,

$5 - \frac{q}{80} - \frac{q}{10} - \frac{q}{80} = 0$

$∴$ $q = 40 μ C$

Potential difference across $C_{1}$

$V = \frac{q}{C_{1}} = \frac{40 \times 10^{- 6}}{10 \times 10^{- 6}} = 4 V$

Now, just after closing the switch $S_{2}$ , charge on each capacitor remains the same.

$V_{P} - 4 - 70 \times 25 \times 10^{- 3} = V_{Q}$

$∴$ $V_{P} - V_{Q} = 4 + 1.75 = 5.75 V$

In loop MPQS,

$+ 10 - 30 i_{1} - 4 - 70 i = 0$

$70 i + 30 i_{1} = 6 \dots (i)$

In loop QROPQ,

$+ 10 - 30 i_{1} + \frac{40}{80} - 5 + (i - i_{1}) \times 130 + \frac{40}{80} = 0$

$130 i - 160 i_{1} = - 6 \dots (i i)$

Solving (i) and (ii), we get

$i = 0.05 A$

$∴$ $i_{1} = 0.077 A$

Solution

Q.
In the circuit shown, initially there is no charge on capacitors and keys $S_{1}$ and $S_{2}$ are open. The values of the capacitors are $C_{1} = 10 μ F$ , $C_{2} = 30 μ F$ and $C_{3} = C_{4} = 80 μ F$ .

Which of the statement(s) is/are correct [2019]

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

2 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 resistor (between points P and Q) will be 0.2 A (round off to $1^{st}$ decimal place).

3 At time $t = 0$ , the key $S_{1}$ is closed, the instantaneous current in the closed circuit will be 25 mA.

4 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 4 V.

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Solution

Q. 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=10 μF, C2=30 μF and C3=C4=80 μF. Which of the statement(s) is/are correct [2019]

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

2 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 resistor (between points P and Q) will be 0.2 A (round off to 1st decimal place).

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