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