# An electric kettle has two heating coils. When one of the coils is connected to an A.C source, the water in the kettle boils in 10 minutes. When the other coil is used the water boils in 40 minutes. If both the coils are connected in parallel, the time taken by the same quantity of water to boil will be: (A) 8 min (B) 4 min (C) 25 min (D) 15 min

Let us suppose, resistance of the two coils be R1 and R2

Voltage supplied = V

Effective resistance of two coils in parallel = (R1.R2) /(R1+R2)

Say, the heat required to begin boiling in kettle is H.

As we know,

H = Power x time

= (V2t1)/R1 = (V2t2)/R2

For parallel combination;

$$H=\frac{V^{2}\left(R_{1}+R_{2}\right) t_{p}}{R_{1} R_{2}}$$

1/tp = (t2 + t1)/(t2.t1)

tp = (t1.t2)/(t1+t2)

= (10 x 40)/(10 + 40)

= 8 minute