Gate 2016 EE – Set 2 – Question 35

Given parameters, $$Z_{11}=40\Omega; Z_{12}=60\Omega; Z_{21}=80\Omega; Z_{22}=100\Omega$$

From the figure,

$$V_{2}=-20I_{2}$$ __________(1)

$$V_{1}=Z_{11}I_{1}+Z_{12}I_{2}$$

$$V_{1}=40I_{1}+60I_{2}$$ _______ (2)

$$V_{2}=Z_{21}I_{1}+Z_{22}I_{2}$$

$$V_{2}=80I_{1}+100I_{2}$$ _________(3)

Substituting (1) into (3), $$-20I_{2}=80I_{1}+100I_{2}$$

$$-120I_{2}=80I_{1}$$

$$I_{2}=\frac{-80}{120}I_{1}=\frac{-2}{3}I_{1}$$

Substituting the above value of $$I_{2}$$ into (2) $$V_{1}=40I_{1}+20\left ( \frac{-2}{3} \right )I_{1}$$

$$V_{1}=40I_{1}-40I_{1}\Rightarrow V_{1}=0$$

From the figure, loop 1 gives us the equation, $$20=10I_{1}+V_{1}$$

$$I_{1}=2A$$

$$I_{2}=\frac{-2}{3}(2)=\frac{-4}{3}A$$

Power dissipated in $$R_{L}=I_{2}^{2}R_{L}$$

$$\Rightarrow \left ( \frac{-4}{3} \right )^{2}\times 20\Rightarrow 35.55W$$