Question

An electric kettle is rated at 200 V and can bring a certain amount of water to its boiling point in 5 minutes. If it is connected to a voltage supply of 180 V, calculate the time in which the same amount of water will reach its boiling point.

Answer 1

(a) Energy consumed by water in 5 min. at 200 V

\[ \mathrm{E}=\frac{\mathbf{V}^{2} \cdot t}{\mathrm{R}}=\frac{200 \times 200 \times 5 \mathrm{~min}}{R} \]

(b) Energy consumed by water at 180 V

\[ \mathrm{E}=\frac{\mathrm{V}^{2} \cdot t}{\mathrm{R}}=\frac{180 \times 180 \times t}{R} \]

∴ By the law of conservation of energy,

\[ \frac{180 \times 180 \times t}{R}=\frac{200 \times 200 \times 5 \mathrm{~min}}{R} \]

\[\therefore t = \frac{200 \times 200 \times 5}{180 \times 180}\text{min}\]

∴ t = 6.17 min