Question

Find the value of $V_x$ (in V) from the network shown below.

• A. 9

Answer 1

The correct option is A 9
From the given network, we can extract some equations which are,

$I_1=15A$ ..........equation (i)

$I_3-I_1=\frac{V_x}{9}$ ...........equation (ii)

$-6I_2+3I_3+2I_1=0$ .............equation (iii)

and
$V_x=3(I_3-I_2)$ .............equation (iv)

Applying KCL at node A,

$I_3=15+\frac{V_x}{9}$

$\Rightarrow I_3=15+\frac{3(I_3-I_2)}{9}$ from equation (iv)

$\Rightarrow I_3=15+\frac{I_3-I_2}{3}$

$\Rightarrow I_3-\frac{I_3}{3}=15-\frac{I_2}{3}$

$\Rightarrow \frac{2I_3}{3}=\frac{45-I_2}{3}$

$\Rightarrow I_2=45-2I_3$ .............equation (v)

Put the value of $I_2$ in equation (iii)

$-6I_2+3I_3+2I_1=0$

$\Rightarrow -6(45-2I_3)+3I_3+2\times 15=0$

$\Rightarrow -270+12I_3+3I_3+30=0$

$\Rightarrow 15I_3$=240

$I_3=16A$

and
$I_2=45-2I_3$
$I_2=45-2\times 16$
$I_2=13A$

From equation (iv)

$V_x=3(I_3-I_2)$
$=3(16-13)$
$=9V$