Alternating Current (A.C)

An alternating current (A.C) is the one that varies sinusoidal in such a way as to reverse its direction periodically.

An a.c is represented by

 I = I_Osinωt = I_Osin2πft

I = instantaneous current 

f= frequency 

ωt= phase angle of the current

ω = angular velocity 

I_O= maximum or peak current 

Also, alternating voltage is

V= V_Osinωt = V_Osin2πft

Peak and r.m.s Values of A.C

The peak value of an a.c current is the maximum value or the amplitude of the a.c current or voltage.

The average value of an a.c current is the sum of the current /voltage above the zero line. The average is zero as it changes between maximum position and negative maximum.

Root mean square (r.m.s) current is that steady current that will develop the same quantity of heat in the same time in the same resistance.

The r.m.s value for the current is

Ir.m.s =  \( \frac {I_0}{\sqrt{2}} \)

Ir.m.s = 0.707I₀

Vr.m.s = 0.707V₀.

Example

An a.c current has a peak value of 4A, calculate: (i) r.m.s current (ii) current at an instant when ωt = 60⁰ and 150⁰

Solution

(i) Ir.m.s = 0.707I₀

       = 0.707 x 4

       = 2.83A

(ii) I = I₀Sinωt

= 4Sin60 = 3.46A

1. I = I₀Sinωt

  = 4Sin150 = 2A