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  4. A capacitor of capacitance 100μF is charged by connecting it to a battery of EMF 12V and internal resistance 2Ω . The time taken before 99 % of the maximum charge is stored on the capacitor-

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Q. A capacitor of capacitance $100μF$ is charged by connecting it to a battery of EMF $12V$ and internal resistance $2\Omega $ . The time taken before $99\%$ of the maximum charge is stored on the capacitor-

NTA AbhyasNTA Abhyas 2020Current Electricity

Solution:

During charging of capacitor, charge at any instant is
$q=q_{0}\left(1 - e^{t / R C}\right)$
$0.99q_{0}=q_{0}\left(1 - e^{- t / R C}\right)$
$0.99=\left(1 - e^{- t / R C}\right)$
$0.01=e^{- t / R C}$
$e^{t / R C}=100$
$t=RCln \left(100\right)$
$t(2)\left(100 \times 10^{-6}\right)(2 \times 2.303)$
$t=0.92 \, ms$