A heater at $220$ $V$ boils a volume of water in $5$ minutes time. If the heater is operated at $110$ $V$ , the same volume of water will boil in $10 n$ minutes. Find the value of $n$ ?

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Solution

Heat $=$ Constant
$\frac{V_{1}^{2}}{R} \cdot t_{1} = \frac{V_{2}^{2}}{R} . \cdot t_{2}$
$\Rightarrow V_{!}^{2} \cdot t_{1} = V_{2}^{2} \cdot t_{2}$
$\Rightarrow t_{2} = {(\frac{V_{1}}{V_{2}})}^{2} \cdot t_{1}$
$\Rightarrow t_{2} = {(\frac{220}{110})}^{2} \times 5 = 20 = 10 \times 2$ $m i n$
$\Rightarrow n = 2$

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