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Lesson 5, Topic 1
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Alternating Current (A.C)

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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

Â I = IOsinÏ‰t = IOsin2Ï€ft

I = instantaneous currentÂ

f= frequency

Ï‰t= phase angle of the current

Ï‰ = angular velocityÂ

IO= maximum or peak current

Also, alternating voltage is

V= VOsinÏ‰t = VOsin2Ï€ft

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 = Â $$\frac {I_0}{\sqrt{2}}$$

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 Ï‰t = 600 and 1500

Solution

(i) Ir.m.s = 0.707I0

= 0.707 x 4

Â Â  Â  Â  = 2.83A

(ii) I = I0SinÏ‰t

= 4Sin60 = 3.46A

1. I = I0SinÏ‰t

Â  = 4Sin150 = 2A

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