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GATE 2014 EC (EC3) – Question 42

Networks, Signals and Systems · Sinusoidal Steady State Analysis · 2 marks · Numerical answer

Find angular frequency ω (rad/s) for which the Norton equivalent impedance seen at b–b′ is purely resistive.

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Correct answer: 1.9 to 2.1

Explanation

Suppress the independent voltage source. The terminal impedance is the series capacitor plus1Ωin parallel with jω/2:Z=−j/ω+(jω/2)/(1+jω/2). Its imaginary part is−1/ω+(ω/2)/(1+ω²/4). Setting this to zero gives ω²/2=1+ω²/4, so **ω=2rad/s**.