Question

Please help?

If the current I in resistor R varies with time t as I=a sint (where a is a constant ).The heat developed in the resistor between t=0 and t=`pi` seconds is

Answer 1

Heat(`dH`) developed in a resistor of resistance `R` in time `dt` is given as `dH = I^2Rdt`(where, `I` is the current flowing through it)

Given, `I=a sint`

So, `dH =R a^2 t sin ^2 t`

so , `int _0^H dH = Ra^2 int _0^pi (t sin ^2 t)`

or, `H = Ra^2 [ (t^2/4)_0^pi - ((t sin 2t)/4)_0^pi -((cos 2t)/8)_0^pi]`

So, `H = Ra^2 (pi^2/4)J`