For the given input voltage waveform

Question:

For the given input voltage waveform $V_{\text {in }}(t)$, the output voltage waveform $\mathrm{V}_{\mathrm{D}}(\mathrm{t})$, across the capacitor is correctly depicted by:


Correct Option: 1

Solution:

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

at $\mathrm{t}=5 \mu \mathrm{s}$

$\mathrm{V}_{0}(\mathrm{t})=5\left(1-\mathrm{e}^{\frac{5 \times 10^{-6}}{10^{3} \times 10 \times 10^{-9}}}\right)$

$=5\left(1-\mathrm{e}^{-0.5}\right)=2 \mathrm{~V}$

Now $\mathrm{V}_{\mathrm{in}}=0$ means discharging

$V_{0}(t)=2 e^{-\frac{t}{R C}}=2 e^{-0.5}$

$=1.21 \mathrm{~V}$

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

$\mathrm{V}_{0}(\mathrm{t})=2.79 \mathrm{Volt} \approx 3 \mathrm{~V}$

Most approperiate Ans.

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