Question 720: 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
2
is ________________.
![](https://imagex.cdn.examgoal.net/1kuckpn5r/34aecc1b-0843-4569-9a8e-f445abb5a5ed/b92e1800-2506-11ec-b291-1df06cb45b25/file-1kuckpn5s.png)

Accepted Answer

Switch at position Q
${V_A} - 1\,.\,{i_2} + 2 - 2{i_2} = {V_A}$
$3{i_2} = 2$
$ \Rightarrow {i_2} = {2 \over 3}A$
Now, ${V_A} - \,{i_2} 	imes 1 = {V_B}$
${V_A} - {V_B} = {i_2} 	imes 1 = {2 \over 3}V$
Potential difference across capacitor, $\Delta V = {2 \over 3}V$
$	herefore$ Charge on capacitor, ${q_2} = C\Delta V = 1 	imes {2 \over 3} = 0.67\mu C$
![](https://app-content.cdn.examgoal.net/fly/@width/image/1l30xuxnr/01eb16b2-4234-4562-926e-5b9db9906faa/ada1df70-d0ce-11ec-bc84-cf2f4c1919d3/file-1l30xuxns.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 2 is ________________.

Integer / Numeric Answer Type