Question

Two electric bulbs have the following specifications.

(i) 100 W at 220 V 

(ii) 1000 W at 220 V.

Which bulb has higher resistance? What is the ratio of their resistances?

Answer 1

The resistance of filament,

\(R=\frac{V}{I}=\frac{V^2}{P}\)

At constant voltage V, the resistance

\(R\,\infty\,\frac{1}{P}\)

That is the resistance of filament of 100 W bulb is greater than that of 1000 W bulb.

The ratio of resistances

\(=\frac{R_1}{R_2}=\frac{P_2}{P_1}=\frac{1000}{100}=\frac{10}{1}=10:1\)