GATE 2021 EE – Question 61
A 100 Hz square wave, switching between 0 V and 5 V, is applied to a CR high-pass filter circuit as shown. The output voltage waveform across the resistor is 6.2 V peak-to-peak. If the resistance R is $820\ \Omega$, then the value C is ________ $\mu$F. (Round off to 2 decimal places.)
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Correct answer: 12.30 to 12.60
Explanation
In steady state the output falls by a factor $a=e^{-T/2\tau}$ during each half-period. Solving for the peaks gives $V_p=V_n=\frac{5}{1+a}$, so the peak-to-peak value is $\frac{10}{1+a}=6.2$ V, which gives $a=0.613$. Then $\frac{T}{2\tau}=-\ln0.613=0.489$, so $\tau=\frac{5\text{ ms}}{0.489}=10.2$ ms and $C=\frac{\tau}{R}=\frac{10.2\text{ ms}}{820\ \Omega}=12.5\ \mu$F.