An electric kettle has two heating coils. When one of the coil is connected to an a.c. source, the water in the kettle boils in 10 minute. 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 minutes (b) 4 minutes (c) 25 minute (d) 15 minute
Let R1 and R2 be the resistance of the two coils and V be the voltage supplied. Effective resistance of two coils in parallel = R1R2/ R1+R2 Let H be the heat required to begin boiling in kettle. Then H= Power × Time = V2t1/ R1 = V2t2/R2 For parallel combination , H= V2(R1+R2)tp/R1R2 1/tp = (t2+t1/t2t1) tp = t1t2/t1+t2 = 10×40/ 10+40 = 8 minutes.
