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GATE 2015 EE - SET 1 - Question 19

Solution :

i =V_{x} ,  I_{1} = i -2 , I_{2} = 10.5i

KCL at node X

I_{1} + i + I_{2}=0

i = \frac{V}{R} = \frac{V_{}x}{1} = V_{x}

I_{1} = \frac{V_{x}-2}{1}  = i-2

I_{2} = \frac{V_{x} -(-20i) }{1}

I_{2}\frac{V_{x} +20 i }{2}

I_{1} + i +I_{2} = 0

(i-2)+ i + (10.5i)=o  ⇒ 12.5i -2 = 0

i =  \frac{2}{12.5} = 0.16 A

I_{2} = 10.5i = 10.5*0.16=1.68A

V_{TH}+V_{AB}= I_{2}R = (16.8)(2) = 3.36V

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