Question

A 500 W heating unit is designed to operate on a 400 V line. If line voltage drops to 160 V, the percentage drop in heat output will be:

• A. 74%
• B. 85%
• C. 84%
• D. 75%

Hint:

The power output of a heating unit is proportional to the square of the voltage. If the voltage decreases, the power output decreases significantly.

Answer 1

The Correct Option is C

The power output of the heating unit is given by the formula: \[ P = \frac{V^2}{R}, \] where: - \( P \) is the power output, - \( V \) is the voltage across the heating unit, - \( R \) is the resistance of the heating unit.
Step 1: Calculate the resistance of the heating unit
For the heating unit designed to operate at 500 W on a 400 V line, we use the formula to find the resistance: \[ 500 = \frac{400^2}{R}. \] Solving for \( R \): \[ R = \frac{400^2}{500} = \frac{160000}{500} = 320 \, \Omega. \]
Step 2: Calculate the power output at the reduced voltage
Now, if the voltage drops to 160 V, the new power output is: \[ P' = \frac{160^2}{R} = \frac{160^2}{320}. \] Substituting the value of \( R \): \[ P' = \frac{25600}{320} = 80 \, \text{W}. \]
Step 3: Calculate the percentage drop in power
The percentage drop in power is given by: \[ \text{Percentage drop} = \frac{500 - 80}{500} \times 100 = \frac{420}{500} \times 100 = 84%. \] Thus, the percentage drop in heat output is 84%, and the correct answer is option (C).