1. Single phase AC Circuits

2. Introduction
Alternating Quantity
An alternating quantity is time dependent or frequency dependent.
The direction changes over every half cycle.
Eg: Time varying voltage, current etc.
i
t
0
i
t
0
i
t
0
The most frequently used form of alternating quantity
is sinusoidal.
Dept of E&E MIT Manipal
ELE101/102

3. Generation of Alternating EMF….
Coil position
0 90 180 270 360
oo o o
GeneratorVoltage
N S
a
b Coil
Rotation Rotation
a
b a b a
b ab a
b
Em
Dept of E&E MIT Manipal
ELE101/102

4. EMF induced per conductor is
e = B l v sinθ
EMF Induced in one Coil is
e = 2 B l v sinθ
If b = width of the coil,
v = π b n
Where ‘n’ is the speed in revolutions per sec.
e = 2 B l b π n sinθ
= 2 B A π n sinθ
If there are N turns in the coil, the
emf induced is,
e= 2 πn B A N sinθ =Emsinθ
Conductorl
b
coil
B
v
Dept of E&E MIT Manipal
ELE101/102
Instantaneous Value of Generated E.M.F.
sinθEe, m=Therefore

5. Important Definitions
Cycle: One complete set of positive and negative values.
Time Period (T): Time duration of a cycle.
Instantaneous Value: Magnitude of the varying quantity at any instant
of time.
Peak Value (Em): Maximum instantaneous value
Frequency (f): Number of cycles in one second. Unit: Hz or cps
One Cycle
π
π/2
2π
e
θ0
Em
e = Emsinθ
T
f 1=
Dept of E&E MIT Manipal
ELE101/102

6. Relation between Frequency and Speed:
Frequency (f) = number of cycles per sec.
f = (No. of Cycles/revolution)*(revolution/Sec)
Let P be the no. of poles in the generator
Then, P/2 cycles of emf is induced per revolution
Therefore,
Relation between frequency and angular frequency:
Where ω = angular frequency in redians /sec.
Then, e = Em sin ωt
Dept of E&E MIT Manipal
ELE101/102
n
P
f *
2
=
fπω 2=

7. Illustration:
A coil of 100 turns is rotated at 1500 rpm in a 2 pole
magnetic field having a uniform density of 0.05 T, the axis
of rotation being at right angles to the direction of the flux.
The mean area per turn is 40 cm2
. Calculate the
a) frequency
b) period
c) maximum value of the generated emf.
d) value of the generated emf. when the coil has rotated through
30° from the position of zero emf.
Ans:
(a) f = 25 Hz
(b) Period = 0.04sec
(c) Em = 3.14V
(d) e = 1.57 V
Dept of E&E MIT Manipal
ELE101/102

8. Phase:
Fraction of Time period elapsed after the alternating quantity last
passed though the zero position of reference
Phase Difference:
Difference of Phase between two alternating quantities.
If waveform 1 is taken as reference;
e1 = Em sinωt
Waveform 2 lags behind waveform1
by an angle Ф
Then, e2 = Em sin(ωt - Ф)
Waveform 3 leads waveform 1
by an angle β
Then, e3 = Em sin(ωt + β)
Dept of E&E MIT Manipal
ELE101/102
Phase & Phase Difference:
0 Ф 180 360-β
1 23
θ