Question

A network of resistances, cell and capacitor $C( = 2 \,\mu F)$ is shown in adjoining figure. In steady state condition, the charge on $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

Answer: (A)

In the steady state, no current will flow through capacitor.
Using Kirchhof's voltage law to the circuit $ACD$

we have, $10-2+1 \times R+1 \times 2=0$
or $R=10 \,\Omega$
Potential diffrence across $C$ and $D$
$V_{C}-V_{D}=2 \times 1=2\, V$
As $V_{D}=0 \,V$
So, $V_{C}=2\, V$
Potential difference across capacitor
$=4-2=2\, V$
$\therefore $ Charge on capacitor
$Q=C V=2 \,\mu F \times 2=4\, \mu C$