Alternating Current

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……………………………………………………………………… 1

            = 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

Also,

            V = V_o sin 2 π ft…………………………………………………………………………………..2

            = V_o sin wt

Examples

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

                     2

            f = 450Hz

           w = 2πf = 900π

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

EVALUATION

1. Differentiate between peak and r.m.s voltage.
2. Calculate the peak and instantaneous voltage of an a.c source represented by; V = 5 sin 500∏t.

Variation of alternating current (or voltage) with time

An alternating current ( or voltage) varies sinusoidally as shown in the diagram above. It is a sine 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:

I_r.m.s.   = I_o

                                 √2 ……………………………………………………. 3    

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.

GENERAL EVALUATION

1.      Differentiate between heat and temperature.

2. Mention five effect of heat.

READING ASSIGNMENT

New School Physics p 447 -457

WEEKEND ASSIGNMENT

1. A 50Hz a.c circuit has a voltage of 220V and a current of 5.0A as its effective value. Determine the peak values of the voltage and its current. (a)311.0V and 1.71A  (b) 331.0V and 7.10A (c)  311.00V and 7.10A(d)7.10V and 311.00A
2. Calculate the peak voltage of a mains supply of r.m.s value of 220V. (a)112V  (b) 150V  (c) 222V (d) 311V
3. In an ac circuit the peak value of the potential difference is 180V. what is the instantaneous  potential differences when the phase angle is 45^o. (a)45V (b) 90V (c) 90√2 V  (d)180V
4. An ammeter connected to an a.c circuit records 5.5A. What is the peak value of the current? (a) 7.8            (b) 7.1              (c) 3.9  (d) 3.
5. When compared, the r.m.s value is ……….  the peak value.(a) greater than(b) same(c) lower than (d) inversely proportional to.

THEORY

1. Distinguish between alternating current (a.c) and direct current (d.c). Explainthe term peak value and 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.