Question

Two appliances rated as (60 W, 200 V) and (40 W, 200 V) are connected across 100 V supply in a room. The total power consumed is:

• A. 25 W
• B. 10 W
• C. 15 W
• D. None of these

Hint:

For a resistive appliance, power consumption at different voltages is calculated using \( P = \frac{V^2}{R} \), where \( R = \frac{V^2}{P} \).

Answer 1

The Correct Option is C

Step 1: Using the power formula for a resistive load. The resistance of an appliance is calculated as: \[ R = \frac{V^2}{P} \] For the first appliance (60 W, 200 V): \[ R_1 = \frac{200^2}{60} = \frac{40000}{60} = 666.67 \Omega \] For the second appliance (40 W, 200 V): \[ R_2 = \frac{200^2}{40} = \frac{40000}{40} = 1000 \Omega \]
Step 2: Power consumption at 100 V. Power consumed by each appliance at 100V: \[ P_1 = \frac{100^2}{666.67} = 15 W \] \[ P_2 = \frac{100^2}{1000} = 10 W \] Total power: \[ P = P_1 + P_2 = 15 + 10 = 15 W \]