An electric kettle has two coils. When one coil is switched an it takes `5` minutes to boil water and when second coil is switched on it takes `10` minutes .How long will it take to boil water, when both the coil are used in series ?

Options

A. 15 min
B. 7.5 min
C. `10/3 min`
D. `2.5 min

Answer

A

Explanation

`(V^2)/(R_1) t_1 = (V^2)/(R_2) t_2 = (V^2)/((R_1+R_2)) t_(1)^(') = (V^2)/((R_1R_2)//(R_1+R_2)) t_(2)^(')`
`(V^2)/(R_1) t_(1) = (V^2)/(R_2) t_(2) implies R_(2) = R_(1)(t_2)/(t_1)`
`(V^2)/(R_1) t_1= (V^2)/((R_1+R_2)) t_(1)^(')`
`(V^2)/(R_1) t_1= (V^2)/((R_(1)+R_(1)(t_(2))/(t_(1)))) t_(1)^(')implies t_(1)^(')=t_(1) (1+(t_2)/(t_1))`
`t_(1)^(') = t_(1)+t_2) = 10+5 = 15 min`.