Question

An electric kettle has two heating elements. One brings it to boil in $10$ min and the other in $15$ min. If two heating elements are connected in parallel, the water in kettle will boil in:

• A. $5min$
• B. $6min$
• C. $7min$
• D. $25min$

Answer 1

The correct option is B $6min$

Assumption: Both the heating elements are supplied with the same potential difference and same mass of water is heated.

Heat supplied is same for both the heating elements when connected individually. Using Joule's Law,

$H_1=H_2$

$\frac{V^2}{R_1}{t}_1=\frac{V^2}{R_2}{t}_2$

$\frac{R_2}{R_1}=\frac{t_2}{t_1}=\frac{15}{10}=1.5$

When connected in parallel, net resistance is:

$R_p=\frac{R_1{R}_2}{R_1+R_2}$

$=\frac{1.5R_1}{2.5}=0.6R_1$

Now, using Joule's law for combination,

$H_1=\frac{V^2}{R_p}t$

$\frac{V^2}{R_1}{t}_1=\frac{V^2}{0.6R_1}t$

$t=6min$