Q 12-03-095JEE MainJEE Main 2024 (8 Apr, Shift 2)Easy
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.
Answer: (A) decreased, $3/4$
The heat needed is the same: $\dfrac{V^2}{R}t = \text{constant}$, so $R \propto t$.
$$\frac{R'}{R} = \frac{15}{20} = \frac34$$
Since $R \propto l$, the length must be decreased to $\frac34$ of its initial value.
Solution by Sreeraj P, M.Sc Physics