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A given quantity of water is boiled by an electric heater in 5 min. If the supply voltage of the heater is reduced to half, the time taken to boil the same quantity of water will be ______ min. (Assume the resistance of the heater remains constant.)

Asked in GUJCET 2016 · Heating and power in resistors

• (1) 10
• (2) 20
• (3) 40
• (4) 2.5

Step-by-step solution

Why the other options are wrong

• (1) Takes the power as proportional to V, so that halving V only doubles the time: 2×5 = 10 min. With R fixed, P = (V²)/R falls to a quarter, so the time becomes four times as long.
• (3) No single slip produces 40 min. Sanity check: P falls exactly to 1/4 of its value, so the time rises exactly fourfold, 4×5 = 20 min.
• (4) Makes the time proportional to the voltage, 5/2 = 2.5 min. A lower voltage means less power, so boiling takes longer, not shorter.

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