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  • For the given i/p voltage waveform the o/p voltage waveform across t

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:-


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\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

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Deependra Verma

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