Question

An electric kettle rated 250 V can bring a certain amount of water to its boiling point in 8 min. If it is connected to a 200 V mains, calculate the time in which the water comes to its boiling point.

Answer 1

(a) Energy consumed by water in 8 min. at 250 V

\[E = \frac{\mathrm{V}^{2} \cdot t}{\mathrm{R}} = \frac{250 \times 250 \times 8 \text{ min}}{\mathrm{R}}\]

(b) Energy consumed by water at 200 V

\[E = \frac{\mathrm{V}^{2} \cdot t}{\mathrm{R}} = \frac{200 \times 200 \times t}{\mathrm{R}}\]

∴ By the law of conservation of energy,

\[\frac{200 \times 200 \times t}{\mathrm{R}} = \frac{250 \times 250 \times 8 \text{ min}}{\mathrm{R}}\]

\[\therefore t = \frac{250 \times 250 \times 8}{200 \times 200} \text{ min}\]

\[\therefore t = 12.5 \text{ min}\]