Question

The power of an electric motor is 242 W when connected to a 220 V supply. When the motor is operated at 200 V, the current drawn by it is

• A. 1.21 A
• B. 1.1 A
• C. 1.5 A
• D. 1 A

Hint:

Always assume resistance is constant for a device unless temperature dependence is mentioned.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The power rating of a device is usually given for a specific voltage to determine its resistance. Assuming the motor acts as a constant resistance load (in the simplified context of such problems unless back EMF is specified), we first find the resistance.
Step 2: Key Formula or Approach:
1. \( P = \frac{V^2}{R} \implies R = \frac{V^2}{P} \). 2. Ohm's Law: \( I = \frac{V_{\text{new}}}{R} \).
Step 3: Detailed Explanation:
Calculate Resistance \( R \) using initial conditions: \( P_1 = 242 \) W, \( V_1 = 220 \) V. \[ R = \frac{V_1^2}{P_1} = \frac{220 \times 220}{242} \] \[ R = \frac{48400}{242} = 200 \, \Omega \] Now, calculate current \( I \) at \( V_2 = 200 \) V: \[ I = \frac{V_2}{R} = \frac{200}{200} = 1 \, \text{A} \]
Step 4: Final Answer:
The current drawn is 1 A.