Water boils in an electric kettle in 20 minutes after being switched on. Using the same main supply, the length of the heating element should be _________ to __________ times of its initial length if the water is to be boiled in 15 minutes.

Solution

Physics sir · 4 steps

Same mains voltage and same heat needed, so the boiling time goes exactly as the element's resistance.

1. Fixed voltage. The mains voltage V stays the same, so use the power form P = V²/R. Boiling the same water needs the same heat H.

   H = V²/R t ⇒ t ∝ R ∝ l

2. Why length. For the same wire, R = (ρ l)/A, so resistance is proportional to length. A shorter element has less resistance, draws more current and gives more power.
3. Take the ratio. l₂/l₁ = t₂/t₁ = 15/20 = 3/4.
4. So. The element must be decreased to 3/4 of its initial length, which is option (c).

The idea to keep. At constant voltage, use P = V²/R, not I²R. Less resistance means more power, so a shorter heating element heats faster.

Answer from the NTA final answer key. Solution by PrepWiser.