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

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Q. 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 MainJEE Main 2022Alternating Current

Solution:

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$ H _1= i ^2 R _1 t \,\, H _2= i _{ rms }^2 R _2 t \left\{ i _{ rms }=\frac{ i _0}{\sqrt{2}}\right\}$
$ H _1=16(3) t \,\,H _2=\frac{ i _0^2}{2} R _2 t$
$ H _2=16 t$
$ H _1: H _2=3: 1$