Question

An electric kettle has two heating coils. When one of the coils is connected to an a.c. source, the water in the kettle boils in 10 minutes. When the other coil is used the water boils in 40 minutes.If both the coils are connected in parallel, the time taken by the same quantity of water to boil will be :

• A. $8min$
• B. $4min$
• C. $25min$
• D. $15min$

Answer 1

The correct option is A $8min$

$Q=\frac{V^2}{R_1}\times t_1=\frac{V^2}{R_2}\times t_2=\frac{V^2}{R}\times t$
$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}\Rightarrow \frac{Q}{V^{2}t}=\frac{Q}{V^2{t}_1}+\frac{Q}{V^2{t}_2}$
$\Rightarrow \frac{1}{t}=\frac{1}{t_1}+\frac{1}{t_2}\Rightarrow t=\frac{t_1{t}_2}{t_1+t_2}$
$=\frac{10\times 40}{10+40}=8$ min.