Average Value of AC

It is that steady DC which would send same amount of charge as is sent by AC when both are allowed to flow independently for half the time period of AC.

Relation b/w Average AC and Peak AC

I = dq/dt

dq = Idt

dq = I₀ sin wt. dt

q = -(I₀/w) [-cos wt]₀^T/2

q = -(I₀/w) [cos(w.(T/2)) – cos w (0)]

q = -I₀/w [cos(π) – cos 0]                         (w = 2π/T)

= -I₀/w [-2]

q = 2I₀/w

q = 2I₀/(2π/T)

q_ac = (2/π).I₀.(T/2)

q_ac = (2/π).I₀.(T/2)

I_dc = q/t

q_dc = I_dc x t

q_d.c = I_d.c x T/2

If q_dc = q_ac

then I_dc  I_avg.

Equating

I_avg.T/2 = (2/π).I₀.(T/2)

I_avg = (2/π).I₀

I_avg = 2/π.I₀

I_avg = 0.636 I₀