Question

An electric kettle has two coils when one of these is switched on the water in the kettle boils in $6min$. When the other coil is switched on, the water boils in $3min$. If the two coils are connected in series, the time taken to boil the water in the kettle is

• A. $3min$
• B. $6min$
• C. $2min$
• D. $9min$

Answer 1

Answer: (D)

$9min$

From Joule's Law of heating:

$\Rightarrow Q=\frac{E^2}{R_1}\times 6..................\left(1\right)$
$Q=\frac{E^2}{R_2}\times 3....................\left(2\right)$
Since heat supplied and applied voltage is same:
$\Rightarrow \frac{3}{R_2}=\frac{6}{R_1}$
$R_1=2R_2$
When the coils are attached in series,

$R=R_1+R_2$
$Q=\frac{E^2}{(R_1+R_2)}\times t$
$Q=\frac{E^2}{3R_2}\times t...............\left(3\right)$
Again, heat supplied and applied voltage is same.

By comparing (2) and (3)

$3=\frac{t}{3}$
$\Rightarrow t=9min$