Question

Voltmeters $V_1$ and $V_2$ are connected in series across a d.c. line. $V_1$ reads 80 V and has a per volt resistance of $200\Omega$, $V_2$ has a total resistance of $32k\Omega$. The line voltage is

• A. 120 V
• B. 160 V
• C. 220 V
• D. 240 V

Answer 1

The correct option is D 240 V


Resistance of voltmeter $V_1$ is $R_1=200\times 80=16000\Omega$ and resistance of voltmeter $V_2$ is $R_2=32000\Omega$
By using relation $V^{{}^{\prime }}=\left(\frac{R^{{}^{\prime }}}{R_{eq}}\right)V$; where V' = potential difference across any resistance R¢ in a series grouping.
So for voltmeter $V_1$ potential difference across it is
$80=\left(\frac{R_1}{R_1+R_2}\right).V\Rightarrow V=240V$