Two lamps, one rated 220 V, 50 W and the other rated 220 V, 100 W, are connected in series with mains of voltage 220 V. Explain why does the 50 W lamp consume more power.

Resistance of lamp A (rating 220 V, 50 W) is —

$R$A = \dfrac{V^2}{PA}

Substituting the values in the formula above we get,

$R$A = \dfrac{220^2}{50} \\[0.5em] \Rightarrow RA = 968 Ω

Resistance of lamp B (rating 220 V, 100 W) is —

$R$B = \dfrac{V^2}{PB}

Substituting the values in the formula above we get,

$R$B = \dfrac{220^2}{100} \\[0.5em] \Rightarrow RB = 484 Ω

From formula, we get, P = I² R

As we observe that R_A > R_B and same current is flowing in both the lamps as both are connected in series therefore P_A > P_B. Hence, 50 W lamp consumes more power than 100 W lamp.