Question

In the circuit shown in figure, reading of voltmeter is \( 80 V \) when only \( S_{1} \) is closed. Reading of voltmeter is \( V_{2} \) when only \( S_{2} \) is closed and reading is \( V_{3} \) when both \( S_{1} \) and \( S_{2} \) are closed. If \( R=12 \Omega \) and resistance of voltmeter is \( R_{V} \), then

Answer 1

When S₁ is closed 

Applying KVL in loop 1

-E + IR + 4IR = 0

5 I R = E

5 I R = 120

I = 120 / 5R

V₁ = I4R

V₁ = \(\frac{120}{5R}\times4R\)

V₁ = \(\frac{480}{5}\)

V₁ = 96 volt

When S₂ is closed 

Applying KVL in loop 2

- E + IR + 12 IR = 0

E = 13 IR

I = \(\frac{120}{13R}\)

V₂ = IR

V₂ = \(\frac{120}{13R}\times 12R\)

V₂ = 110.7 volt