Question

An electric kettle has two thermal coils A and B. When current is passed through A, water in kettle boils in 6 mins. When current is passed through coil B, same volume of water in the kettle boils in 8 mins. If both A and B would be joined in series and current would be passed, water would boil in how many minutes?

Answer 1

Let the resistance of coil 1 and coil 2 be R1and R2

Heat produced by the coil 1, H1 = V^2 (6min)/ R1 ....(1)

Heat produced by the coil 2, H2 = V^2(8min)/ R2 ....(2)

H1 = H2

⇒ R2 = 4R1 /3

Series:

H = V^2t'/R

R = R1 + R2 = 7R1 /3

H = 3V^2t'/7R1 ...(3)

Dividing equation (3) by (1)

t' = 14 min