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7.Alternating Current
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At $t = 0$ , switch $S$ is closed. The charge on the capacitor is varying with time $t$ as $Q\ =\ {Q_0}\left( {1 - {e^{ - \alpha t}}} \right)$ . Find the value of $Q_0$
A
$\frac{{CV{R_2}}}{{{R_1} + {R_2}}}$
B
$\frac{{CV{R_1}}}{{{R_1} + {R_2}}}$
C
$\frac{{CV{R_1}{R_2}}}{{\left( {{R_1} - {R_2}} \right)\left( {{R_1} + {R_2}} \right)}}$
D
None
Solution
$\mathrm{Q}_{0}$ is charge on the capacitor at $\mathrm{t}=\infty$
At $t=\infty,$ No current in capacitor, $\Delta v$ across
Capacitor $=\frac{\mathrm{v}}{\mathrm{R}_{1}+\mathrm{R}_{2}} \mathrm{R}_{2}$
Hence $\mathrm{Q}_{0}=\frac{\mathrm{CVR}_{2}}{\mathrm{R}_{1}+\mathrm{R}_{2}}$
Standard 12
Physics
