GATE 2015 EE – SET 1 -Quesion 46

Solution :

$$V_{1}$$ = 10 V , $$I_{2}$$ = 4A, $$V_{1}$$=5V , $$I_{2}$$=1.25 ,$$ R_{2}$$=15 L , $$V_{1}$$=3V , $$R_{2}$$ = 25 L , $$I_{2}$$ = ?

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

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

When port 2 short circuits , ⇒ $$V_{2}$$=0

$$y_{21}$$ = $$\frac{I_{2}}{V_{1}}$$ =$$ \frac{4}{10} $$= 0.4

For the second case  ; $$V_{1 } $$= 5 , $$I_{2}$$=1.25 , $$R_{2}$$=1 , $$y_{21}$$ = 0.4

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

1.25 = (0.4)5  + $$y_{22}$$ (1.25)

$$y_{22}$$ = -0.6

Third case :

$$V_{1}$$=3V , $$I_{2}$$ = ? ,$$R_{2}$$ = 2Ω

$$V_{2}$$= 2$$I_{2}$$

$$I_{2}$$ + (0.4)(3) + (-0.6) (2$$I_{2}$$)

$$I_{2}$$ = 0.545 A