Question

A vessel has two electrical coils connected in parallel. When one coil is switched on it takes $30$ minutes to boil a given amount of water. When other coil is switched on it takes $60$ minutes to boil same water. If both coils are switched on simultaneously, what time will it take to boil same amount of water?

• A. $30$ minutes
• B. $20$ minutes
• C. $10$ minutes
• D. $40$ minutes

Answer 1

The correct option is B $20$ minutes

Let $H$ be the amount of heat required to boil the given water.

$H=\frac{V^2}{R_1}{t}_1\Rightarrow \frac{V^2}{R_1}=\frac{H}{t_1}$
$H=\frac{V^2}{R_2}{t}_2\Rightarrow \frac{V^2}{R_2}=\frac{H}{t_2}$

When two coils are switched on,

$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}$
$\Rightarrow \frac{V^2}{R}=\frac{V^2}{R)1}+\frac{V^2}{R_2}$
$\Rightarrow \frac{H}{t}=\frac{H}{t_1}+\frac{H}{t_2}$
$\Rightarrow \frac{1}{t}=\frac{1}{t_1}+\frac{1}{t_2}$
$\Rightarrow t=\frac{t_1\times t_2}{t_1+t_2}=\frac{30\times 60}{30+60}=20\text{min}$