Question

An electrical bulb rated $220\text{V}$, $100\text{W}$, is connected in series with another bulb rated $220\text{V},60\text{W}$. If the voltage across combination is $220\text{V}$, the power
consumed by the $100\text{W}$ bulb will be about ____ $\text{W}$.

Answer 1

$P_{100}=\frac{V^2}{R_{100}}\Rightarrow R_{100}=\frac{V^2}{P_{100}}$

$P_{60}=\frac{V^2}{R_{60}}\Rightarrow R_{60}=\frac{V^2}{P_{60}}$

$P_{net}=\frac{V^2}{R_{60}+R_{100}}=\frac{P_{60}{P}_{100}}{p_{60}+P_{100}}=\frac{60\times 100}{160}=37.5$

This power developed is proportional to resistance.

So, power developed is proportional to resistance.

So, $P_{60}^{\prime }=P_{net}\times \frac{60}{100}=37.5\times \frac{60}{160}\simeq 14\text{W}$