Question

It takes 16 min to boil some water in an electric kettle. Due to some defect it becomes necessary to remove 10% turns of the heating coil of the kettle. After repairs, how much time will it take to boil the same mass of water?

• A. 17.7 min
• B. 14.4 min
• C. 20.9 min
• D. 13.7 min

Answer 1

The correct option is B 14.4 min

If N is the initial number of turns in the coil and r is the radius of coil, the resistance of it is
$R=\frac{\rho L}{A}=\frac{\rho N\left(2\pi r\right)}{A}$
Heat, $H=ms\Delta T=\frac{A{V}^2}{N\left(2\pi r\right)}t$
So $t\propto N$
Thus, $\frac{t_1}{t_2}=\frac{N_1}{N_2}$
Here, $N_1=N$ and $N_2=N-\left(N/10\right)=0.9N$
So, $t_2=\frac{N_2}{N_1}{t}_1=\frac{0.9N}{N}\times 16=14.4min$