A direct current of 4 A and an alternating current of peak value 4 A flow through resistance of $3 \Omega$ and $2 \Omega$ respectively. The ratio of heat produced in the two resistances in same interval of time will be :

JEE Main · 2022 · 27 Jul 2022 · Shift 1 · Current Electricity

A direct current of 4 A and an alternating current of peak value 4 A flow through resistance of

3Ω

and

2Ω

respectively. The ratio of heat produced in the two resistances in same interval of time will be :

Answer: (B)

Heat produced by DC:

H_{1} = i^{2} R_{1} t = (4)^{2} \times 3 \times t = 48 t

. For AC, the rms current is

i_{rms} = i_{0} / 2 = 4/ 2

, so heat produced is

H_{2} = i_{rms}^{2} R_{2} t = (16/2) \times 2 \times t = 16 t

. The ratio

H_{1} : H_{2} = 48 t : 16 t = 3 : 1

JEE Main · 2022 · 27 Jul 2022 · Shift 1 · Single correct option