Question

Voltmeters V1 and' V2 are connected in series across a D.C. line. V1 reads 80 V and has a per volt resistance of 200 $\Omega$, V2 has a total resistance of 32 $\Omega$. 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

In this case, the resistance across the second voltmeter V2 is given as 32 ohms and the resistance across the first resistor V1 is calculated as follows.
The resistance per unit volt is 200 ohms and the total number of volts is 80 V. Therefore, the resistance across the voltmeter V1 is $Resistanceperunitvolt\times Totalvolts=200\times 80=16000K$.
The line voltage is calculated using the formula, $V1=\left(\frac{V}{R1+R2}\right)R1$
So, $V=V1\times \left(\frac{R1+R2}{R1}\right)=\frac{80\times (16+32)}{16}=240V$.
Hence, the line voltage is 240 V.