Question

Water boils in an electric kettle in $15$ minutes after switching on. If the length of the heating wire is decreased to $2 / 3$ of its initial value, then the same amount of water will boil with the same supply voltage in

• A. 15 minutes
• B. 12 minutes
• C. 10 minutes
• D. 8 minutes

Answer 1

Answer: (C)

$H=\frac{V^{2}}{R} t$
Since supply voltage is same and equal amount of heat will be produced, therefore
$\frac{R_{1}}{t_{1}}=\frac{R_{2}}{t_{2}}$ or $\frac{R_{1}}{R_{2}}=\frac{t_{1}}{t_{2}}$ ......(i)
But $R \propto l \Rightarrow \frac{R_{1}}{R_{2}}=\frac{l_{1}}{l_{2}}$ .........(ii)
By (i) and (ii),
$\frac{l_{1}}{l_{2}}=\frac{t_{1}}{t_{2}}$ ....... (iii)
Now $l_{2}=\frac{2}{3} l_{1} \Rightarrow \frac{l_{1}}{l_{2}}=\frac{3}{2}$
$\therefore $ By equation (iii), $\frac{3}{2}=\frac{15}{t_{2}} \Rightarrow t_{2}=10$ minutes