Show that average heat produced during a cycle of `AC` is same as produced by `DC` with `i=i_("rms")`.

Explanation

For an `AC,i=i_0sinomegat`
Therefore, instantaneous value of heat produced in time `dt` across a resistance `R` is
`:. dH-i^2Rdt=i_0^2Rsin^2omegatdt`
`:.` Averge value of the produced during as cycle,
`H_(av) =(int_0^TdH)/(int_0^Tdt)=(int_0^(2pi/omega)(i_0^2Rsin^2omegat)dt)/(int_0^(2pi//omega)dt)`
`i_0^2/2R((2pi)/omega)=i_(rms)i^2RT`
i.e. `AC` produces same heating efects as `DC` of value `i=i_(rms)`