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(D) The heat energy $H$ required to heat the water is given by the formula $H = \frac{V^2 t}{R}$,where $V$ is the voltage,$t$ is the time,and $R$ is t

Vedclass · Accepted Answer

$20$

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(D) The heat energy $H$ required to heat the water is given by the formula $H = \frac{V^2 t}{R}$,where $V$ is the voltage,$t$ is the time,and $R$ is the resistance of the heater.Since the amount of water and the required temperature rise are the same,the heat energy $H$ remains constant. Also,the resistance $R$ of the heater is constant.Therefore,$V^2 t = 	ext{constant}$,which implies $t \propto \frac{1}{V^2}$.We can write the ratio as $\frac{t_1}{t_2} = \left( \frac{V_2}{V_1} ight)^2$.Given $V_1 = 220 \, 	ext{V}$,$t_1 = 5 \, 	ext{min}$,and $V_2 = 110 \, 	ext{V}$.Substituting the values: $\frac{5}{t_2} = \left( \frac{110}{220} ight)^2 = \left( \frac{1}{2} ight)^2 = \frac{1}{4}$.Thus,$t_2 = 5 	imes 4 = 20 \, 	ext{min}$.

An electric heater heats a certain amount of water in $5 \, \text{min}$ when connected to a $220 \, \text{V}$ supply. How many minutes will it take to heat the same amount of water when connected to a $110 \, \text{V}$ supply?

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