# For the given i/p voltage waveform $V_{in}(t)$ the o/p voltage waveform $V_{0}(t)$ across the capacitor is correctly depicted by:- Option: 1 Option: 2 Option: 3 Option: 4

$\mathrm{V}_{0}(\mathrm{t})=\mathrm{V}_{\mathrm{in}}\left(1-\mathrm{e}^{-\frac{\mathrm{t}}{\mathrm{RC}}}\right) at t=5 \mu s \\ \mathrm{V}_{0}(\mathrm{t})=5\left(1-\mathrm{e}^{-\frac{5 \times 10^{-6}}{10^{3} \times 10 \times 10^{-9}}}\right) \\ =5\left(1-\mathrm{e}^{-0.5}\right)=2 \mathrm{~V} \\ Now \mathrm{V}_{\text {in }}=0 means discharging \\ \\ V_{0}(t)=2 e^{-\frac{t}{R C}}=2 e^{-0.5} =1.21 \mathrm{~V}$

$\\ \text{Now for next} \ 5 \mu \mathrm{s} \mathrm{V}_{0}(\mathrm{t})=5-3.79 \mathrm{e}^{-\frac{\mathrm{t}}{\mathrm{RC}}} \\ after 5 \mu \mathrm{s} again V_{0}(t)=2.79 Volt \approx 3 V$

Most approperiate Ans.(1)

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