Question

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

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

Answer 1

The correct option is D $240V$

As voltmeter $V_1$ has value $80V$ and has a per volt resistance of $200\Omega$.

Thus total resistance across voltmeter $V_1,$ $R_1=80\times 200\Omega$

$⟹$ $R_1=16k\Omega$

Resistance across voltmeter $V_2,$ $R_2=32k\Omega$

Total resistance of series connection $R_s=R_1+R_2$

$\therefore$ $R_s=16k\Omega +32k\Omega =48k\Omega$

Let the line voltage be $E$.

Using $V_1=\frac{R_1}{R_s}E$

$\therefore$ $80=\frac{16}{32}E$

$⟹$ $E=240V$