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

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 R1 and R2 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 P1 and P2 be the power dissipated by two bulbs, turn

P1‘ = i2 R1 and P2‘= i2 R2

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

or P1‘ = 5 P2

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