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Gate 2016 EE - Set 2 - Question 34

Driving point input impedance, is defined as ratio of emf of source to the current of the source.

Z_{d}=\frac{V_{s}}{I_{s}}
V_{1}=2I_{s}

V_{A}=V_{s}-V_{1}

V_{A}=V_{s}-2I_{s}

Applying KCL at A, I_{s}+4V_{1}-\frac{V_{A}}{3}-\frac{V_{A}}{6}=0

I_{s}+4V_{1}-\frac{3V_{A}}{6}=0

I_{s}+4V_{1}-\frac{V_{A}}{2}=0

I_{s}+4(2I_{s})-\frac{(V_{s}-2I_{s})}{2}=0

2I_{s}+16I_{s}-V_{s}+2I_{s}=0

\frac{V_{s}}{I_{s}}=20\Omega

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