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In the given circuit initially the capacitor is uncharged. At t=0 the key is closed. Choose the correct options (s)

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The time constant of the circuit is . $\frac{11 R C}{5}$

The time constant of the circuit is . $\frac{11 R C}{4}$

current through the capacitor after one time constant is $\frac{3 E}{11 R} (\frac{1}{e})$

current through the capacitor after one time constant is $\frac{5 E}{11 R} (\frac{1}{e})$

answer is A, C.

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Detailed Solution

Equivalent resistance across capacitor (after shorting the battery) $= \frac{11 R}{4}$ .
Voltage across capacitor in steady state $= \frac{3 E}{4}$
$q = \frac{C E}{4} (1 - e^{\frac{- 4 t}{11 R C}})$

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