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 $armV_{3}$
$\frac{x - 8}{R}=\frac{8 - 0}{G}$
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