An electric kettle has two coils. When one coil is switched on, it takes 15 minutes to boil water, and when the second coil is switched on, it takes 30 minutes. How long will it take to boil water if booth coils are sued, in series and a parallel, respectively ?

45 min, 10 min

Let Power of coils are P₁ and P₂ respectively then 

$R_1= \frac{V^2}{P_1} \text{ and } R_2  = \frac{V^2}{P_2} \text{ respectively.}$

$ t_1 = \frac{H}{P_1}$

$ t_2 = \frac{H}{P_2}$

In series combination $P_s = \frac{V^2}{R_1+R_2} = \frac{V^2}{\frac{V^2}{P_1} + \frac{V^2}{P_2}} = \frac{P_1P_2}{P_1+P_2}$

$ t_s = \frac{H}{P_s} = \frac{H}{P_1} + \frac{H}{P_2} = t_1+ t_2 = 45 min$

In Parallel Combination$ P = P_1 + P_2 $

$ t_p = \frac{H}{P} = \frac{H}{P_1 + P_2} = \frac{t_1t_2}{t_1+t_2} = 10min.$