Question

An immersion heating rod is rated at 220 V and can bring a certain amount of water to its boiling point in 15 min. When this immersion rod is actually connected to an electric circuit, it brings the water to a boil in 18.15 min. Calculate the line voltage.

Answer 1

(a) Energy consumed by water in 15 min. at 220 V

\[E = \frac{\mathrm{V}^{2} \cdot t}{\mathrm{R}} = \frac{220 \times 220 \times 15 \text{ min}}{\mathrm{R}}\]

(b) Energy consumed by water at line voltage V

\[E = \frac{V^{2} \times 18.15 \text{ min}}{\mathrm{R}}\]

∴ By the law of conservation of energy,

\[\frac{V^{2} \times 18.15 \text{ min}}{\mathrm{R}} = \frac{220 \times 220 \times 15 \text{ min}}{\mathrm{R}}\]

\[V^{2} = \frac{220 \times 220 \times 15}{18.15}\]

\[V = \sqrt{\frac{220 \times 220 \times 15}{18.15}}\]

\[V = 220 \times \sqrt{\frac{15}{18.15}}\]

\[V = 220 \times \sqrt{\frac{15 \times 100}{1815}}\]

\[V = 220 \times \sqrt{\frac{100}{121}}\]

\[V = 220 \times \frac{10}{11}\]

\[\therefore V = 200 \text{ V}\]