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GATE 2021 EE – Question 30

Electric Circuits · Transient response of DC and AC networks, sinusoidal steady-state analysis, resonance, two port networks, balanced three phase circuits, star-delta transformation, complex power and power factor in AC circuits · 1 mark · Numerical answer

The Bode magnitude plot for the transfer function $\dfrac{V_o(s)}{V_i(s)}$ of the circuit is as shown. The value of R is ________ $\Omega$. (Round off to 2 decimal places.)

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Correct answer: 0.09 to 0.11

Explanation

The circuit is a series RLC low-pass filter with output across the capacitor. The resonant frequency $\omega_0=\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{1\text{ mH}\times250\ \mu\text{F}}}=2000$ rad/s agrees with the plot. The peak of 26 dB means $Q=10^{26/20}\approx20$. Since $Q=\frac1R\sqrt{\frac LC}=\frac{2}{R}$, $R=\frac{2}{20}=0.10\ \Omega$.