Question

A room heater is rated 400 W, 220 V. If the supply voltage drops to 200 V, what will be the power consumed (approximately)? ____.

• A. 121 W
• B. 200 W
• C. 400 W
• D. 331 W

Hint:

You can also use the ratio method: $\frac{P_2}{P_1} = \left(\frac{V_2}{V_1}\right)^2$. This avoids calculating $R$ explicitly and reduces the chance of rounding errors in the middle of the problem.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The resistance ($R$) of the heater is a property of the material and remains constant even if the voltage changes. Power ($P$) consumed depends on the square of the voltage.

Step 2: Key Formula or Approach:
1. $R = \frac{V^2}{P}$ (Using rated values) 2. $P_{new} = \frac{V_{new}^2}{R}$

Step 3: Detailed Explanation:
1. Find Resistance ($R$): \[ R = \frac{220^2}{400} = \frac{48400}{400} = 121\,\Omega \] 2. Calculate New Power ($P_{new}$): \[ P_{new} = \frac{200^2}{121} = \frac{40000}{121} \] \[ P_{new} \approx 330.57\,\text{W} \approx 331\,\text{W} \]

Step 4: Final Answer:
The power consumed at 200 V is approximately 331 W.