Question

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?

• A. \(P_B = 124.8 \, \text{W}, P_H = 33.25 \, \text{W}\)
• B. \(P_B = 33.25 \, \text{W}, P_H = 124.8 \, \text{W}\)
• C. \(P_B = 124.8 \, \text{W}, P_H = 124.8 \, \text{W}\)
• D. \(P_B = 33.25 \, \text{W}, P_H = 33.25 \, \text{W}\)

Hint:

For series combinations, the total power is divided between the components according to their resistances.

Answer 1

The Correct Option is A

Let the resistances of the heater and bulb be \(R_H\) and \(R_B\), respectively. The power consumed by the heater and bulb in series can be calculated using: \[ P_H = \frac{V^2}{R_H}, \quad P_B = \frac{V^2}{R_B} \] The total resistance of the series combination is \(R_{total} = R_H + R_B\). The total power supplied is: \[ P_{total} = \frac{V^2}{R_{total}} \] By substituting the values and solving for individual powers, we get: \[ P_B = 124.8 \, \text{W}, P_H = 33.25 \, \text{W} \]