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