Question

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.

• A. increased, $\frac{3}{4}$
• B. increased, $\frac{4}{3}$
• C. decreased, $\frac{3}{4}$
• D. decreased, $\frac{4}{3}$

Answer 1

Answer: (C)

decreased, $\frac{3}{4}$

Answer 2

The resistance of the heating element is:
$R = \rho \frac{\ell}{A}.$
The power is inversely proportional to the length:
$P \propto \frac{1}{\ell}.$
From the relation $P_1 \times t_1 = P_2 \times t_2$:
$\frac{P_1}{P_2} = \frac{t_2}{t_1} = \frac{15}{20}.$
Substituting $P \propto \frac{1}{\ell}$:
$\frac{\ell_2}{\ell_1} = \frac{t_2}{t_1} = \frac{15}{20} = \frac{3}{4}.$
Thus, the new length should be decreased to:
$\ell_2 = \frac{3}{4} \ell_1.$