Question

The network of the figure shown consists of resistive network described as$y_{11}=y_{22}=y_{21}=2\mho and{Y}_{12}=1\mho$, then the value of voltage $V_1$ is

• A. $\frac{7}{9}V$
• B. $\frac{9}{7}V$
• C. $\frac{9}{2}V$
• D. $\frac{2}{9}V$

Answer 1

The correct option is D $\frac{2}{9}V$

From given y -parameters,

$I_1=2V_1+V_2$
$I_2=2V_1+2V_2$

Using nodal analysis,
$I_1+\frac{V_1-V_2}{0.5}+\frac{V_1}{2}=1$ ...(i)

and $I_2+\frac{V_2-V_1}{0.5}+\frac{V_2}{2}=0$ ...(ii)

substitute the value of $I_2$ in equation (ii),
$2V_1+2V_2+2V_2-2V_1+V_2=0$

$\Rightarrow V_2=0$
substitute the value of $I_1$ in equation (i),
$2V_1+V_2+2V_1-2V_2+0.5V_1=1$

$\Rightarrow 4.5V_1=1$

$V_1=\frac{1}{4.5}=\frac{2}{9}V$