Introduction to Electric Circuits

4.1 Alternating quantities 67

It follows that

f- 1/T (4.1)

Example 4.1

Determine (1) the periodic time of an a.c. quantity of frequency 50 Hz, (2) the

frequency of an a.c. waveform for which the period is 2.5 ms.

Solution

1 From Equation (4.1), f= lIT so that T = l/f= 1/50 = 20 ms.

2 Again from Equation (4.1), f= lIT = 1/(2.5 • 10, 3) = 400 Hz.

There is an enormous range of frequencies and they are banded as shown in

Table 4.1.

Table 4.1

Frequency range Description

• 20 Hz Low
  20 Hz - 15 kHz Audio
  15 kHz - 30 kHz Very low radio
  30 kHz - 300 kHz Low radio
  300 kHz - 3 MHz Medium radio
  3 MHz- 30 MHz High radio
  30 MHz- 300 MHz Very high (VHF)
  300 MHz- 3 GHz Ultra high (UHF)
  3 GHz - 30 GHz Super high

Instantaneous values

In general an alternating quantity changes its magnitude from instant to instant

over the cycle time and these values are called the instantaneous values of the

quantity. They are represented by lower case letters, for example i (for

current), v (for voltage).

Peak values

The highest value reached by a quantity in the cycle is called the maximum (or

peak or crest) value. This value is usually denoted by a capital letter with a

circumflex accent or with a subscript max or m so that a peak voltage might be

written 9 or Vmax or Vm.

Sinusoidal a.c. quantities

The beauty of a.c. is that the voltage and current levels can be easily changed by