Question

Two heater coils separately take 10 min and 5 min to boil a certain amount of water. If both the coils are connected in series, the time taken will be

• A. 2.5 min
• B. 3.33 min
• C. 7.5 min
• D. 15 min

Answer 1

Answer: (D)

15 min

Let, resistances of two coils are $R_1$ and $R_2$ then
$\frac{V^2\left(10\right)}{R_1}=Jms\Delta \theta$
and
$\frac{V^2\left(5\right)}{R_2}=Jms\Delta \theta$

Hence,
$\frac{V^2\left(10\right)}{R_1}=\frac{V^2\left(5\right)}{R_2}$
$\therefore R_1=2R_2$

When both the coils are connected in series,

$\frac{V^2\left(t\right)}{R_1+R_2}=Jms\Delta \theta$

$\frac{V^2\left(t\right)}{R_1+R_2}=\frac{V^2\left(5\right)}{R_2}$

$\frac{V^2\left(t\right)}{3R_2}=\frac{V^2\left(5\right)}{R_2}$

$t=15min$