SINGLE PHASE A.C CIRCUITS

ELECTRICAL ENGG SCIENCE CHAPTER - 6

CONTENT

1. Generation of alternating voltage and current

2. Different forms of E.M.F equations.

3. A.C through R, L and C and power factor

4. A.C through R,R-C and R-L series and parallel circuits

5. Active and reactive components of circuit & Active, reactive and

apparent power.

What is A.C?

An alternating current (a.c) is the current which changes

periodically both in magnitude and direction.

Different A.C. waveforms

Cycle

One complete set of positive and negative values of alternating

quantity is known as cycle.

Time Period

The time taken by an alternating quantity to complete one cycle

is called its time period T.

Frequency

The number of cycles/second is called the frequency of the

alternating quantity. Its unit is hertz(Hz)

Also or

Amplitude

The maximum value, positive or negative, of an alternating

quantity is known as its amplitude.

Generation of alternating voltage and current

The machine which are used to generate electrical voltages are

called generators. The generators which generate purely sinusoidal a.c.

voltages are called ALTERNATORS.

Generation of alternating voltage and current

Basic principle of an alternator is the principle of electromagnetic

induction. The sine wave is generated according to FARADAY’S LAW OF

ELECTROMAGNETIC INDUCTION.

Faraday’s Law of Electromagnetic Induction

Whenever there is a relative motion between the conductor and

the magnetic field in which it is kept, an e.m.f. gets induced in the

conductor.

The relative motion may exist because of movement of

conductors with respect to magnetic field or movement of magnetic

field with respect to conductor.

Let us see how an alternator produces a sine wave, with the help

of simplest form of an alternator called single turn or single loop

alternator.

Different forms of E.M.F equationsThe standard form of an alternating voltage is given by,

Different forms of E.M.F equations

R.M.S Value

The r.m.s value of an alternating current is given by that steady

current (d.c) which, when flowing through a given time, produces the

same amount of heat as produced by the alternating current, which

when flowing through the same circuit for the same time.

R.M.S Value

Average Value

The average value of an alternating quantity is defined as that

value which is obtained by averaging all the instantaneous values over a

period of half cycle.

Form Factor (Kf)

Peak Factor (KP)

PhaseThe phase of an alternating quantity at any instant is the angle Ф

(in radians or degrees) travelled by the phasor representing that

alternating quantity upto the instant of consideration, measured from

the reference.

Phase

Phase Difference (In Phase)

Phase Difference (Lag)

Phase Difference (Lead)

Phasor Diagram

In phase

Apparent Power (S)

It is defined as the product of r.m.s value of voltage (V) and

current (I). It is denoted by S.

It is measured in unit volt-amp (VA) or kilo volt-amp (kVA).

Real or True Power (P)

It is defined as the product of applied voltage and active

component of the current. It is real component of the apparent power.

It is measured in unit watts (W) or kilo watts (kW).

Reactive Power (Q)

It is defined as product of the applied voltage and the reactive

component of the current. It is represented by Q.

It is measured in unit Volt-Amp Reactive (VAR) or kilo Volt-Amp

Reactive (kVAR)

Power Factor

It is defined as factor by which the apparent power must be

multiplied in order to obtain the true power.

It is the ratio of true power to apparent power.

Power Factor

It is also defined as the ratio of resistance to the impedance.

KEYPOINT: Nature of power factor is always determined by position of

current with respect to the voltage.

Power Factor

If current lags voltage power factor is said to be lagging. If

current leads voltage power factor is said to be leading.

A.C through R

Current

Phasor Diagram

Power

A.C through L

Current

Phasor Diagram

Power

A.C through C

Current

Phasor Diagram

Power

AC through RL series circuit

Impedance

Power

AC through RC series circuit

Power