Question

The circuit shown consists of three identical resistances and three identical voltmeters. Reading of first and third voltmeters are $V_1=22$ volt and $V_3=8$ volt. Calculate the reading of second voltmeter.

• A. $4$ volt
• B. $8$ volt
• C. $12$ volt
• D. $20$ Volt

Answer 1

Answer: (C)

Let internal resistance of the voltmeters be $G$ .

Applying Kirchoff's Current law,
$\frac{22-x}{R}=\frac{x-8}{R}+\frac{x-0}{G}$
and in $arm{V}_3$
$\frac{x-8}{R}=\frac{8-0}{G}$
Therefore, $\frac{22-x}{R}=\frac{x-8}{R}+\frac{x}{8}\times \frac{x-8}{R}$
$\Rightarrow 176-8x=x^2-64$
$\Rightarrow x^2+8x-240=0$
$\Rightarrow x=\frac{-8\pm \sqrt{64+960}}{2}$
$\Rightarrow x=-4+\sqrt{16+240}$
$\Rightarrow x=-4+\sqrt{256}=-4+16=12$ volt