Question 718: Electrostatics & Capacitance

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
$\mu$C. Then S is switched to position Q. After a long time, the charge on the capacitor is q
2
$\mu$C.
The magnitude of q
1
is ________________.
![](https://imagex.cdn.examgoal.net/1kuckpn5r/34aecc1b-0843-4569-9a8e-f445abb5a5ed/b92e1800-2506-11ec-b291-1df06cb45b25/file-1kuckpn5s.png)

Accepted Answer

Switch connected to position P
${V_A} - 1\,.\,{i_1} - 1 + 2 - 2{i_1} = {V_A}$
$3{i_1} = 1$
${i_1} = {1 \over 3}A$
Now, ${V_A} - 1\,.\,{i_1} - 1 = {V_B}$
${V_A} - {V_B} = 1 + {i_1} = {4 \over 3}V$
Potential drop across capacitor, $\Delta V = {4 \over 3}V$
$	herefore$ Charge on capacitor, ${q_1} = C\Delta V = 1 	imes {4 \over 3}\mu C$
${q_1} = 1.33\mu C$
![](https://app-content.cdn.examgoal.net/fly/@width/image/1l30xz9r4/5b17bc2c-6528-4339-825a-aa0e7bd70813/2635f200-d0cf-11ec-9372-d31f6f396ecf/file-1l30xz9r5.png?format=png)

Electrostatics & Capacitance

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 \muC. Then S is switched to position Q. After a long time, the charge on the capacitor is q 2 \muC. The magnitude of q 1 is ________________.

Integer / Numeric Answer Type