GATE EE 2021 Set 1 — Question 61
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Electric Circuits → Transient & AC Steady-State → First-Order RL & RC
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Question
A square wave, switching between and , is applied to a CR high-pass filter circuit as shown. The output voltage waveform across the resistor is peak-to-peak. If the resistance is , then the value is ________ . (Round off to 2 decimal places.)
Correct answer
12.3 to 12.6
Solution
The input is a square wave of period that jumps by (from to and back). Let and .Steady-state output across
- A capacitor voltage cannot change instantly, so at every input edge the output jumps by the full input step: at a rising edge, at a falling edge.
- Between edges the input is constant, so decays exponentially towards with time constant .
- In steady state the output has no DC component, so it is symmetric: just after a rising edge , just after a falling edge .
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