A residential electric range has a nameplate rating of 12 kW at 240 volts. If this range is connected to a 208-volt single-phase supply, what will be the approximate power consumption?
Because the physical heating element doesn't change, its resistance stays the same. When voltage drops, power drops with the square of the voltage (P is proportional to E²), not in straight proportion. Method 1 (The Short Way): Square the voltage ratio. (208V / 240V)^2 = 0.751. Multiply by original power: 12 kW * 0.751 = 9.01 kW. Method 2 (The Long Way): First, find the element's fixed resistance using R = E^2 / P. (240V)^2 / 12,000W = 4.8 ohms. Now, apply the new voltage to that resistance using P = E^2 / R. (208V)^2 / 4.8 ohms = 9,013 Watts (9.0 kW).
Did you pick 10.4 kW? You fell for the trap! You can't just use a straight percentage because power is based on the SQUARE of the voltage. Master those two formulas: R = E^2 / P and P = E^2 / R.