AC Fundamentals – Notes

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Generation of Alternating Voltages and Currents

Alternating voltage may be generated by rotating a coil in a magnetic field, or by rotating a magnetic field within a stationary coil.

The value of the voltage generated depends, in each case, upon the number of turns in the coil, strength of the field and the speed at which the coil or magnetic field rotates. Alternating voltage may be generated in either of the two ways.

Cycle

One complete set of positive and negative values of alternating quantity is known as cycle. Hence, each diagram of Fig. 11.6 represents one complete cycle.

A cycle may also be sometimes specified in terms of angular measure. In that case, one complete cycle is said to spread over 360⁰ or 2π radians.

Time Period

The time taken by an alternating quantity to complete one cycle is called its time period T. For example, a 50-Hz alternating current has a time period of 1/50 second

Frequency

The number of cycles/second is called the frequency of the alternating quantity. Its unit is hertz (Hz).

It may be noted that the frequency is given by the reciprocal of the time period of the alternating quantity.

∴ f = 1/T or T = 1/f

Amplitude

The maximum value, positive or negative, of an alternating quantity is known as its amplitude.

Phase

The fraction of the time period of that alternating current which has elapsed since the current last passed through the zero position of reference.

Root-Mean-Square (R.M.S.) Value

The r.m.s. value of an alternating current is given by that steady (d.c.) current which when flowing through a given circuit for a given time produces the same heat as produced by the alternating current when flowing through the same circuit for the same time.

Average Value

The average value of an alternating current is expressed by that steady current which transfers across any circuit the same charge as is transferred by that alternating current during the same time.

Form Factor

It is defined as the ratio, K­_f = r.m.s. value/average value = 0.707 I­_m /0.637 I­_m = 1.1 (for sinusoidal alternating currents only).

In the case of sinusoidal alternating voltage also, Kf = 0.707 ­E_m /0.637 E­_m = 1.1 (for sinusoidal alternating currents only).

Crest or Peak or Amplitude Factor

It is defined as the ratio K­_a = maximum value/r.m.s. value
= I­_m /(I­_m /√2) = √2 = 1.414 (for sinusoidal a.c. only).

For sinusoidal alternating voltage also, K­_a = IE_m /(E_m /√2) = √2 = 1.414 (for sinusoidal a.c. only).

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