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

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

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

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

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

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