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A network of resistances, cell and capacitor $\mathrm{C}(=2 \mu \mathrm{F})$ is shown in adjoining figure.In steady state condition, the charge on $2 \mu \mathrm{F}$ capacitor is $Q$, while $R$ is unknown resistance. Values of $Q$ and $R$ are respectively
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$4 \mu \mathrm{C}$ and $10 \Omega$
In the steady state, current through capacitor
Using Kirchhof's voltage law to the circuit ACD
We have, $10-2+1 \times \mathrm{R}+1 \times 2=0$ or $\mathrm{R}=10 \Omega$
Potential difference across $\mathrm{C}$ and $\mathrm{D}$
$\mathrm{V}_{\mathrm{C}}-\mathrm{V}_{\mathrm{D}}=2 \times 1=2 \mathrm{~V}$
As $\mathrm{V}_{\mathrm{D}}=0 \mathrm{~V}$
So, $V_{C}=2 V$
Potential difference across capacitor $=4-2=2 \mathrm{~V}$
$\therefore$ Chargeon capacitor $\mathrm{Q}=\mathrm{CV}=2 \mu \mathrm{F} \times 2=4 \mu \mathrm{C}$
Using Kirchhof's voltage law to the circuit ACD
We have, $10-2+1 \times \mathrm{R}+1 \times 2=0$ or $\mathrm{R}=10 \Omega$
Potential difference across $\mathrm{C}$ and $\mathrm{D}$
$\mathrm{V}_{\mathrm{C}}-\mathrm{V}_{\mathrm{D}}=2 \times 1=2 \mathrm{~V}$
As $\mathrm{V}_{\mathrm{D}}=0 \mathrm{~V}$
So, $V_{C}=2 V$
Potential difference across capacitor $=4-2=2 \mathrm{~V}$
$\therefore$ Chargeon capacitor $\mathrm{Q}=\mathrm{CV}=2 \mu \mathrm{F} \times 2=4 \mu \mathrm{C}$
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