Q: A 100 W and a 500 W bulbs are joined in series and connected to the mains. Which bulb will glow brighter ?

Sol. Let R_{1} and R_{2} be the resistances of the bulbs. If each bulb is connected separately to the mains of

voltage V,

Then $\large P_1 = \frac{V^2}{R_1}$ and $\large P_2 = \frac{V^2}{R_2}$

$\large \frac{P_1}{P_2} = \frac{R_2}{R_1}$

or, $\large \frac{R_1}{R_2} = \frac{P_2}{P_1} = \frac{500}{100} = 5 $

If the two bulbs are in series with the mains, the same current ‘i’ flows through each of them.

Let P_{1} and P_{2} be the power dissipated by two bulbs, turn

P_{1}‘ = i^{2} R_{1} and P_{2}‘= i^{2} R_{2}

$\large \frac{P_1′}{P_2′} = \frac{R_1}{R_2} = 5 $

or P_{1}‘ = 5 P_{2}‘

Since 100 watt bulb dissipates more power, it glows brighter.