What is meant by mean or average value of alternating current ? Show that mean value of ac over a complete cycle is zero.

Explanation

At any time, alternating current flowing through the circuit is given by
`I= l_0 sinomegat`
Let dq = Small amount of charge sent by a.c. in small time dt
Suppose current I remains constant for time dt
`:. dq = I dt`
`dq = I_0 sin omegat dt ` [Using.eq. (1)]
Charge sent by a.c. over a complete cycle is
`intdq=int_0^TI_0sinomegat dt`
`q=I_0|(-cosomegat)/(omega)|_0^T`
`q=I-_0/omega|cosomegaT-costheta|`
`q=I_0/omega|cos""(2pi)/T(T)-1|" "[ :. omega=(2pi)/T]`
`q=I_0/(omega)|1-1|=0`
Let `I_(av)` = .Mean value of a.c. over the complete cycle.
Then charge sent by it is given by
`q= _(av) (T) " "....(ii)`
From eqns. (i) and (ii)
`I_(av) (T)=0`
`I_(av) =0`
So mean value of a:c: over a complete cycle is zero.