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GATE 2017 EE (EE2) – Question 31

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

For the shown two-port network, the transfer impedance $z_{21}$ in ohms is ________.

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Correct answer: 3 to 3

Explanation

By definition, $z_{21}=V_2/I_1$ with the output port open, I2=0. The direct 4 Ω path from port 1 to the centre is parallel to the upper 2 Ω plus right 2 Ω path, also 4 Ω.

Input current divides equally between these paths and then all passes through the centre-to-ground 2 Ω resistor. The centre voltage is 2I1. The output is above it by $(I_1/2)(2)=I_1$.

Thus V2=3I1 and **$z_{21}=3\ \Omega$**.

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