Question

A network of resistances, cell and capacitor $C(=2\mu F)$ is shown in adjoining figure. In steady state condition, the charge $2\mu F$ capacitor is $Q$. while $R$ is unknown resistance. Values of $Q$ and $R$ are respectively

• A. $4\mu C$ and $10\Omega$
• B. $4\mu C$ and $4\Omega$
• C. $2\mu C$ and $2\Omega$
• D. $8\mu C$ and $4\Omega$

Answer 1

The correct option is A $4\mu C$ and $10\Omega$

Given,

In the steady state, current through capacitor

Using Kirchhof's voltage law to the circuit ACD

In ACD ,$V_1+V_2+V_3+V_4=0$

We have, $10-2+1\times R+1\times 2=0$

Or $R=10\Omega$
Potential difference across C and D
$V_C-V_D=2\times =2V$
As, $V_D=0V$
So, $V_C=2V$
Potential difference across capacitor
$=4-2=2V$
$\therefore$ Charge on capacitor $Q=CV=2\mu F\times 2=4\mu C$