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