Question

Two 220 volt lamps, one of 60 watt and the other of 75 watt are connected in series across a 440 volt supply. The potential difference across 60 watt lamp will be:
1. 195 volt
2. 220 volt
3. 245 volt
4. 440 volt

Answer 1

Correct Answer - Option 3 : 245 volt

Concept:

Power of the lamp is given by

Power = (Voltage)2 / Resistance

⇒ Resistance = (Voltage)² / Power

⇒ R = (V²) / P

Calculation:

Given, 

P₁ = 60 W, P₂ = 75 W

V₁ = 220 V, V₂ = 440 V

Resistance of 60 W lamp  be R₁

Resistance R₁ = (V₁)² / P₁

⇒ R₁ = (220)² / 60 = 806.67 Ω 

Resistance of 75 W lamp be R₂

Resistance R₂ = (V₁)² / P₂

⇒ R₂ = (220)² / 75 = 645.34 Ω 

Now both are connected in series, the voltage across the 60 W lamp is

\({V_{60W}} = {V_2} \times \left( {\frac{{{R_1}}}{{{R_1} + {R_2}}}} \right) = 440 \times \left( {\frac{{806.67}}{{806.67 + 645.37}}} \right)\)

⇒ V_60W = 244.44 ≈ 245 V

Therefore the voltage across 60 W bulb is 245 V