Electric Circuit Analysis: Unit I: b. Basic circuits analysis

Some important terms

Wave form, Cycle, Time period, Frequency, Amplitude | Basic circuits analysis

Wave form : It is the graph drawn between the alternating quantity (only instantaneous value) as ordinate and time as abscissa.

SOME IMPORTANT TERMS

 

(i) Wave form

It is the graph drawn between the alternating quantity (only instantaneous value) as ordinate and time as abscissa.

The alternating quantity may be either voltage or current or flux. Accordingly, the wave form is known as voltage wave form, current wave form or flux wave form. There are many types of wave forms. Some examples are

(a) Sinusoidal wave form,

(b) Rectangular wave form,

(c) Triangular wave form

(d) Saw-tooth wave form

(e) Trapezoidal wave form

(f) Stepped wave form and so on.

Assuming the alternative quantity to be the voltage, the wave forms for the above cases are plotted below.


Note:

1. Only few types of wave forms are shown above.

2. The reader must be able to draw the wave form when its equation is given.

3. He or she must also be able to write the equation when the wave form is given.

4. Our discussion is confined only to sinusoidal wave form. The definition for various other terms are confined to sinusoidal wave form.

 

(ii) Cycle

It is a set of positive and negative portions of wave form


 

(iii) Time period

The time required for an alternating quantity to complete one cycle is called the time period and is denoted by T.

 

(iv) Frequency

The number of cycles per second is called frequency and is denoted by f. It is measured in cycles/second (cps) or Hertz (Hz).

From definitions of T and f, we can write that

f = 1 / T

 

(v) Amplitude

The maximum value of the alternating quantity in a cycle, is called amplitude. It is also known as peak value or crest value. In the voltage wave form shown in Fig (1.75), the peak value is Em. It is obtained when the angle is π/2  (positive cycle) and 3π/2 (negative cycle).

Relation between ω and f

Angular distance = angular velocity × time

i.e., θ = ω × t ... (4)

When θ = 360° = 2π radians, one cycle is completed.

Then time t = time taken for completion of one cycle = T. Substituting these values in equation (4) we get

2π = ωT

ω 2π / T

ω 2πf

 

Electric Circuit Analysis: Unit I: b. Basic circuits analysis : Tag: : Wave form, Cycle, Time period, Frequency, Amplitude | Basic circuits analysis - Some important terms