A room heater is rated 750 W, 220 V. An electric bulb rated 200 W, 220 V is connected in series with this heater. What will be the power consumed by the bulb and the heater respectively, when the supply is at 220 V?

$P_B=124.8 W, P_H=33.25 W$

The correct answer is Option (1) → $P_B=124.8 W, P_H=33.25 W$

Power (P) is given by,

$Power=\frac{[Voltage(V)]^2}{Resistance (R)}$

$⇒R_{Heater}=\frac{{V_{Heater}}^2}{P_{Heater}}=\frac{220^2}{750}=\frac{48400}{750}≃64.53Ω$

$⇒R_{bulb}=\frac{{V_{bulb}}^2}{P_{bulb}}=\frac{220^2}{200}≃242Ω$

and,

$R_{total}=R_{Heater}+R_{bulb}$

$=64.53+242=306.53Ω$

$I=\frac{V_{total}}{R_{total}}=\frac{220}{306.53}≃0.718A$

$∴P_{Heater}=I^2R_{Heater}=(0.718)^2×64.53≃33.2W$

$P_{bulb}=I^2R_{bulb}=(0.718)^2×242≃124.5W$