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Q. For the given input voltage waveform $V _{\text {in }}( t )$ the output voltage waveform $V _{ o}( t )$, across the capacitor is correctly depicted by:
image

JEE MainJEE Main 2020Alternating Current

Solution:

image
$V _{0}( t )= V _{\text {in }}\left(1- e ^{-\frac{1}{ RC }}\right)$
at $t=5 \mu s$
$V _{0}( t )=5\left(1- e ^{\frac{5 \times 10^{-6}}{10^{3} \times 10 \times 10^{-9}}}\right)$
$=5\left(1- e ^{-0.5}\right)=2 V$
Now $V _{\text {in }}=0$ means discharging
$V _{0}( t )=2 e ^{-\frac{ t }{ RC }}=2 e ^{-0.5}$
$=1.21 V$
Now for next $5 \mu s$
$V _{0}( t )=5-3.79 e ^{-\frac{1}{ RC }}$
after $5 \mu s$ again $V_{0}$
$(t)=2.79$ Volt $\approx 3 V$