A capacitor of capacity \( 1 \mu \mathrm{F} \) is connected in a cl...

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A capacitor of capacity \( 1 \mu \mathrm{F} \) is connected in a closed series circuit with a resistance of \( 10^{7} \mathrm{ohms} \), an open key and a cell of \( 2 \mathrm{~V} \) with negligible internal resistance:
If after completely charging the capacitor, the cell is shorted by zero resistance at time \( t=0 \), find the charge on the capacitor at \( \mathrm{t}=50 \mathrm{~s} \). (Given : \( \mathrm{e}^{-5}=6.73 \times 10^{-3}, \ell \mathrm{n} 2=0.693 \) )
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