Gate 2016 EE Set 2 – Question 37

$$V_{ci}=4V; t=25\mu s to t=100\mu s$$

$$i(t)=\frac{V}{R}e^{\frac{-t}{\tau }}$$

$$i(t)=\frac{4}{5}e^{\frac{-t}{\tau }}$$

Where, $$\tau =RC=(5)(5\times 10^{-6})=25\times 10^{-6}sec$$

$$\int_{25\mu s}^{100\mu s}i(t)dt=\int_{25\mu s}^{100\mu s}\frac{4}{5}e^{\frac{-t}{25\times 10^{-6}}}$$

$$\Rightarrow 6.99\times 10^{-6}C \Rightarrow 6.99\mu C$$