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प्रश्न
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.
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उत्तर
(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,
\[\frac{V^{2} \times 18.15 \text{ min}}{\mathrm{R}} = \frac{220 \times 220 \times 15 \text{ min}}{\mathrm{R}}\]
\[V^{2} = \frac{220 \times 220 \times 15}{18.15}\]
\[V = \sqrt{\frac{220 \times 220 \times 15}{18.15}}\]
\[V = 220 \times \sqrt{\frac{15}{18.15}}\]
\[V = 220 \times \sqrt{\frac{15 \times 100}{1815}}\]
\[V = 220 \times \sqrt{\frac{100}{121}}\]
\[V = 220 \times \frac{10}{11}\]
\[\therefore V = 200 \text{ V}\]
