A resistive water-heater element is rated 4,800 watts at 240 volts. If it is connected to a 208-volt supply, approximately how much power will it produce?
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Answer: A
- Givens: P = 4,800 W at 240 V; new supply = 208 V; the load is resistive, so R is constant.
- Resistance: R = V² ÷ P = 240² ÷ 4,800 = 57,600 ÷ 4,800 = 12 Ω.
- New power: P = V² ÷ R = 208² ÷ 12 = 43,264 ÷ 12 ≈ 3,605 W.
- Check: (208 ÷ 240)² = 0.751, and 0.751 × 4,800 ≈ 3,605 W.
3,605 watts: Correct. The element's resistance stays fixed at 240² ÷ 4,800 = 12 ohms, so at 208 volts P = 208² ÷ 12 ≈ 3,605 watts; power falls with the square of the voltage.
4,160 watts: This scales the power in direct proportion to voltage (4,800 × 208 ÷ 240); for a fixed resistance, power varies with voltage squared.
4,800 watts: This assumes the rated wattage is delivered at any voltage; the rating applies only at 240 volts.
5,538 watts: This inverts the voltage ratio (4,800 × 240 ÷ 208), as if lower voltage raised the power.
For a fixed resistance, power is proportional to the square of the voltage: a 240-V element on 208 V gives about 75% of its rated watts.