Question

Voltmeters V₁ and V₂ are connected in series across a d.c. line. V₁reads 80 V and has a per volt resistance of 200 Ω, V₂ has a total resistance of 32 kΩ. The line voltage is

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

Answer 1

Answer: (D)

240 V

Answer 2

Resistance of voltmeter V₁ is R₁ = 200 × 80 = 16000 Ω and resistance of voltmeter V₂ is R₂ = 32000 Ω

By using relation $V' = \left( \frac{R'}{R_{eq}} \right)V;$ where V′ = potential difference across any resistance R′ in a series grouping.

So for voltmeter V₁ potential difference across it is

$80 = \left( \frac{R_{1}}{R_{1} + R_{2}} \right).V$ ⇒ V = 240 V