Category: 6. AC Fundamentals
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ADDITION AND SUBTRACTION OF ALTERNATING QUANTITIES
In AC circuits, it is required to add or subtract the alternating quantities. In such cases, it should be proceed as follows: 6.19.1 Addition of Alternating Quantities The given alternating quantities are represented as phasor, and then, they are added in the same manner as forces are added. Only phasors of the similar quantities are…
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PHASE AND PHASE DIFFERENCE
The phase of an alternating quantity (current or voltage) at an instant is defined as the fractional part of a cycle through which the quantity has advanced from a selected origin (Fig. 6.23). In actual practice, we are more concerned withthe phase difference between the two alternating quantities rather than their absolutephase. Fig. 6.23 Phasor representation…
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FORM FACTOR AND PEAK FACTOR
There exists a definite relation among the average value, rms value, and peak value of an alternating quantity. The relationship is expressed by the two factors, namely form factor and peak factor. Example 6.1 The equation of an alternating current is i = 42.42 sin 628 t Determine (i) its maximum value; (ii) Frequency; (iii) rms value; (iv)…
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RMS VALUE OF SINUSOIDAL CURRENT
An alternating current varying sinusoidally is given by the following equation: i = Im sin θ To determine the rms value, the squared wave of the alternating current is drawn as shown in Figure 6.11. Fig. 6.11 Squared-wave shape of a sine wave Considering an elementary strip of thickness dθ in the first half-cycle of the squared wave, let i2 be…
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EFFECTIVE OR RMS VALUE
The steady current when flows through a resistor of known resistance for a given time produces the same amount of heat as produced by an alternating current when flows through the same resistor for the same time is called effective or rms value of an alternating current. Let i be an alternating current flowing through a resistor…
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AVERAGE VALUE OF SINUSOIDAL CURRENT
The alternating current varying sinusoidally, as shown in Figure 6.9, is given by the equation: i = Imsinθ Fig. 6.9 Current varying sinusoidally Consider an elementary strip of thickness dθ in the positive half cycle, i be its mid-ordinate. Then, Area of strip = idθ Area of half cycle = Im[–1(–1–1)] = 2Im Base = 0 to π = π − 0 = π ∴ Average value,
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PEAK VALUE
The maximum value attained by an alternating quantity during one cycle is called ‘peak value’. This is also called ‘maximum value or crest value or amplitude’. A sinusoidal alternating quantity obtains its maximum value at 90° as shown in Figure 6.7. The peak of an alternating voltage and current is represented by Em and Im. The knowledge of…
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VALUES OF ALTERNATING VOLTAGE AND CURRENT
The voltage and current in DC system are constant so that there is no problem of specifying their magnitudes, whereas in AC system, the alternating voltage and current vary from time to time. Hence, it is necessary to explain the ways to express the magnitude of alternating voltage and current. The following three ways are…
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DIFFERENT FORMS OF ALTERNATING VOLTAGE EQUATION
The alternating voltage is given by the following standard equation: e = Em sin θ or e = Em sin ω t or e = Em sin 2 π ft (sin ω = 2π f) = Em sin 2 πt/T (since f = 1/T) Which form of the above equation is to be applied will depend upon the data given? To determine the various values, for example, maximum value, frequency, time period, angular velocity, etc., the given equation is compared…
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IMPORTANT RELATIONS
Some of the terms used in AC terminology have definite relations among themselves as given below: