A capacitor of capacitance C=1 uF is suddenly connected to a battery of 100 volt

Question:

A capacitor of capacitance $\mathrm{C}=1 \mu \mathrm{F}$ is suddenly connected to a battery of 100 volt through a resistance $R=100 \Omega$. The time taken for the capacitor to be charged to get $50 \mathrm{~V}$ is :

$[$ Take $\ln 2=0.69]$

  1. $1.44 \times 10^{-4} \mathrm{~s}$

  2. $3.33 \times 10^{-4} \mathrm{~s}$

  3. $0.69 \times 10^{-4} \mathrm{~s}$

  4. $0.30 \times 10^{-4} \mathrm{~s}$


Correct Option: , 3

Solution:

$\mathrm{V}=\mathrm{V}_{0}\left(1-\mathrm{e}^{-\frac{\mathrm{t}}{R C}}\right)$

$50=100\left(1-e^{-\frac{t}{R C}}\right)$

$\mathrm{t}=0.69 \times 10^{-4} \mathrm{sec}$

Leave a comment