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# A capacitor is charged to $3200 V$ and then connected across a resistor of resistance R. If after 1 s potential difference across capacitor is 2400 V, What will be the potential difference across after 2 and 3 seconds .

$(A)\;1600\; and\; 80 V \\ (B)\;1800\; and\;1350V \\ (C)\; 2000\; and\;1800V \\ (D)\;1400\;and\; 200V$

$V= V_0 e^{-t/cR}$
=> $2400 =3200 e^{-1/cR}$
=> $e^{-1/Rc}=\large\frac{3}{4}$
For $t=2s$
$V= 3200 e^{-2/RC}$
$\qquad= 3200 \bigg( \large\frac{3}{4} \bigg) \bigg( \large\frac{3}{4} \bigg)$
$\qquad= 1800 V$
For $t=3s$
$V= 3200 e^{-3/RC}$
$\qquad= 3200 \bigg( \large\frac{3}{4} \bigg)^3$
$\qquad= 1350 V$
Hence B is the correct answer.

edited Jul 31, 2014