The magnitude of q1 is ______. [2021]

Question

In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes $q_{1} μ C$ . Then S is switched to position Q. After a long time, the charge on the capacitor is $q_{2} μ C$ .

Q. The magnitude of $q_{1}$ is ______. [2021]

Smart Achievers · Accepted Answer

(1.33)

$When the switch is connected to position P$

From KVL,

$V_{A} - 1 \cdot i_{1} - 1 + 2 - 2 i_{1} = V_{A} \Rightarrow 3 i_{1} = 1$ $∴$ $i_{1} = \frac{1}{3} A$

Again, $V_{A} - 1 \cdot i_{1} - 1 = V_{B}$ or, $V_{A} - V_{B} = 1 + i_{1} = \frac{4}{3} V$

Potential drop across the capacitor, $Δ V = \frac{4}{3} V$

$∴$ $Charge on capacitor, q_{1} = C Δ V = 1 \times \frac{4}{3} μ C$

$q_{1} = 1.33 μ C$

$When the switch is connected to position Q$

From KVL,

$V_{A} - 1 \cdot i_{2} + 2 - 2 i_{2} = V_{A}$ $\Rightarrow 3 i_{2} = 2$ $∴$ $i_{2} = \frac{2}{3} A$

Again, $V_{A} - i_{2} \times 1 = V_{B}$

$V_{A} - V_{B} = i_{2} \times 1 = \frac{2}{3} V$

Potential difference across the capacitor, $Δ V = \frac{2}{3} V$

$∴$ $Charge on capacitor, q_{2} = C Δ V = 1 \times \frac{2}{3} μ C$

$q_{2} = 0.67 μ C$

Solution

Q.
In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes $q_{1} μ C$ . Then S is switched to position Q. After a long time, the charge on the capacitor is $q_{2} μ C$ .

Q. The magnitude of $q_{1}$ is ______. [2021]

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Solution

Q. In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes q1 μC. Then S is switched to position Q. After a long time, the charge on the capacitor is q2 μC. Q. The magnitude of q1 is ______. [2021]

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Q.
In the circuit shown below, the switch S is connected to position P for a long time so that the charge on the capacitor becomes $q_{1} μ C$ . Then S is switched to position Q. After a long time, the charge on the capacitor is $q_{2} μ C$ .

Q. The magnitude of $q_{1}$ is ______. [2021]