AC FUNDAMENTALS – PART – 01 – IMPORTANT TERMS AND ADVANTAGES OF SINE WAVEFORM

ALTERNATING VOLTAGE AND CURRENT

1. Alternating current periodically changes the direction in which it is flowing.

2. It also changes magnitude either continuously or periodically.

3. An alternating voltage is a voltage which produces an alternating current when used to power circuit.

4. Most types of alternating current, the magnitude is changing continuously.

5. The AC power refers to power that is produced by alternating current and alternating voltage.

6. Alternating quantities may be represented graphically. The curve obtained by plotting the values of voltage or current at different instants on vertical axis and time or angle on horizontal axis is called a waveform.

7. Most common type of waveform is sine wave. It is an alternating waveform in which sin law is followed.

8. Non-sinusoidal waveform is an alternating waveform in which sine law is not followed.

9. Periodic waveform is one which repeats itself after definite time intervals.

10. Alternating current can be electronically produced in an almost infinite variety of waveform.

TYPES OF A.C. WAVEFORMS

• The alternating current and voltage supplied to homes and factories is sinusoidal.
• Square wave form is used extensively in computer circuits.
• Sawtooth waveform is used in television receivers, radar receivers and other electronic devices.
• Electronic music is created by producing and mixing together a wide variety of waveforms.

ADVANTAGES OF SINE WAVEFORM

In any natural object which has a periodic motion such as a swinging pendulum, a vibrating string or the rippling surface of a body of water, we find this form of wave. The sine curve is apparently nature’s standard. Circular motion produces a sine wave naturally.

The sine wave greatly simplifies the theory and calculations of a.c. circuits. For this reason, the designers of a.c. generators try always to obtain a waveform approximating as closely as possible to that of a pure sine wave.

• The sine wave can be expressed in a simple mathematical form.
• The rate of change of any sinusoidal quantity is also sinusoidal.
• When current in a capacitor, in an inductor or in a transformer is sinusoidal, the voltage across the element is also sinusoidal. This is not true of any other waveform.
• The mathematical computation, connected with alternating current work, are much simpler with this waveform.
• By means of Fourier series analysis, it is possible to represent any periodic function of whatever waveform in terms of sinusoids.

IMPORTANT TERMS

1. Cycle – One complete alternation or repletion of a set of values of current is called a cycle.

2. Alternation – One-half cycle of an alternating quantity is called alternation. An alternation spans 180 degree electrical.

3. Period – The time required to complete one cycle is called the periodic time or simply the period (T).

4. Frequency – The number of cycles completed in one second is called the frequency (f). The unit of frequency is the hertz.

One hertz = One cycle per second.

5. Amplitude – The maximum value positive or negative attained by an alternating quantity is called its amplitude or peak value. The amplitude of an alternating voltage or current is noted by Vm or Im

IMPORTANT RELATIONS

1. Time period and frequency [f = 1/T Hz]

2. Angular velocity and frequency [2πf = 2π/T in radians /sec.]

3. Frequency, speed and number of poles [f = PN/120]

f = frequency in Hertz, T = Time period in sec.

N = Revolution per minute and P = No. of poles.

VALUES OF ALTERNATING QUANTITIES

1. Instantaneous value – The value of an alternating quantity at a given instant (time) is called instantaneous value. It varies from instant to instant. It is denoted by small letters v or i.

2. Maximum or crest value – This is the maximum value of the alternating quantity attained by it in a cycle. It is the highest of the instantaneous values. It is denoted by a capital letter and a subscript m (Vm or Im).

3. Average or mean value – The average value of a waveform is the average of all its values over a period of times.

Average value

= [Total (net) area under curve for time T] / [Time T]

Average value of a symmetrical wave

= [Area of one alternation] / [Base length of one alternation]

Average value of an unsymmetrical wave

= [Area over one cycle] / [Base length of one cycle]

4. Effective value – The effective value of an alternating current is that value that produces the same heat in a resistive circuit as a direct current of the same value. Also, equal amounts of dc voltage and effective ac voltage produce equal power across resistors of equal value.

5. RMS value – The effective value of a waveform can be determined by a mathematical process known as Root Mean Square (RMS) value.