Question

An electric kettle has two heating coils. When one coil is used, water
in the kettle boils in $5\text{minutes}$, while when second coil is used, the
same water boils in $10\text{minutes}$. If the two coils, connected in parallel are used simultaneously, the same water will boil in

• A. $7\text{min}30s$
• B. $30\text{min}20s$
  
• C. $2\text{min}30s$
  
• D. $5\text{min}$
  

Answer 1

The correct option is B $30\text{min}20s$


Let the power rating of first coil be $P_1$ and second coil be $P_2$.

Also, let the heat required by water to reach boiling point be $H$.

Given, time required by coil 1 to heat water,

$t_1=\frac{H}{P_1}=5\text{min}$

Time required by coil 2 to heat water,

$t_2=\frac{H}{P_2}=10\text{min}$

Since power required for heating is inversely proportional to resistance,

$\therefore$ Total power delivered in parallel combination $\left(P\right)$ ,

$\Rightarrow P=P_1+P_2$

So, time taken by water to boil in this combination is

$\Rightarrow t=\frac{H}{P}=\frac{H}{P_1+P_2}$

$\Rightarrow t=\frac{H}{\frac{H}{5}+\frac{H}{10}}=\frac{5\times 10}{10+5}=\frac{50}{15}$

$\Rightarrow t=3.33\text{min}$

$\Rightarrow t=3\text{min}20s$

Hence, option (a) is correct.