Question

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

• A. 6.66 mim
• B. 7.5 mim
• C. 3.33 min
• D. 2.5 min

Answer 1

The correct option is C 3.33 min

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

and $\frac{V^2\left(5\right)}{R_2}=Jms\Delta \theta$
$R_2=\frac{5V^2}{Jms\Delta \theta }$

If both the coils are connected in parallel
$\frac{\left(R_1{R}_2\right)}{R_1+R_2}=\frac{V^{2}t}{Jms\Delta \theta }$

$t=\frac{Jms\Delta \theta \left(R_1{R}_2\right)}{V^2(R_1+R_2)}$

$t=\frac{Jms\Delta \theta \left(\frac{10V^2}{Jms\Delta \theta }\right)\left(\frac{5V^2}{Jms\Delta \theta }\right)}{V^2(\frac{10V^2}{Jms\Delta \theta }+\frac{5V^2}{Jms\Delta \theta })}$

if we put all the given value then we get ,
$t=\frac{\left(10\right)\left(5\right)}{(10+5)}$

$t=3.33min$