Lesson Notes By Weeks and Term - Senior Secondary School 2

Alternating Current Circuit







TOPIC: Alternating Current Circuit


Alternating Current Circuit

Graphical Representation

Peak and R.M.S. Values

A.C circuits are circuits through which an alternating current flows. Such circuits are used extensively in power transmission, radio and television, computer technology, telecommunication and in medicine. It varies sinusoid ally or periodically, in such a way as to reverse its direction periodically. The commonest form of such a.c can be represented by 

    I = Io sin 2π ft

    = Io sin wt

I is the instantaneous current at a time t, Io is the maximum ( or peak ) value of current or its amplitude; f is the frequency and w = (  2π ft) us the angular velocity, (wt) is the phase angle of the current 


    V = Vo sin 2 π ft

       = Vo sin wt


If an a.c voltage is represented by 1f 

V =  4 sin 900 πt, calculate the peak and instantaneous voltage 

The peak voltage, Vo = 4v

    2πft  = 900πt

    F = 900


    f = 450Hz

           w = 2πf = 900π

Peak, and r.m.s. values of a.c

Variation of alternating current ( or voltage) with time.

An alternating current ( or voltage) varies sinusoidally as shown in the diagram above. It is asine waveform . the amplitude or peak value of the current Io is the maximum numerical value fo the current.

The root mean square (r.m.s) value of the current is the effective value of the the current . it is that steady current which will develop the same quantity of heat in the same time in the same resistance.

The r.m.s. value for the current is given by:

  1. r.m.s.   = Io

                                       √2  = 0.707%.

The moving iron and hot wire meters measure the average value of the square of the current called the mean-square current .  they are however calibrated in such a way as to indicate the r.m.s. current directly. This most a.c meters read the effective or r.m.s. values. The average value of an a.c voltage is zero.

Reading Assignment

New School Physics p 447 -457


  1. Distinguish between alternating current (a.c) and direct current (d.c). Explainthe term peak valueand r.m.s. value as they apply to a.c circuit
  2. Draw a wave from diagram for an a.c and label the  points at which the current is zero and maximum respectively. Determine the effective value of an a/c if its peak value is 15A.

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