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}= 2I_{2}

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

I_{2} = 0.545 A