- The document discusses alternating current (AC) and its generation using a simple AC generator. AC voltage and current change polarity and magnitude at regular time intervals. - Key terms related to AC quantities are defined, including cycle, time period, frequency, peak value, average value, and root mean square (RMS) value. The frequency of power supply in India is 50 Hz. - Behavior of AC circuits containing resistance, inductance, and capacitance is examined. Current and voltage are in phase for resistance. For inductance, current lags voltage by 90 degrees, while for capacitance current leads voltage by 90 degrees.

1. PEE-102A
Fundamentals of Electrical Engineering
Lecture-5
Instructor:
Mohd. Umar Rehman
EES, University Polytechnic, AMU
March 30, 2021
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2. Alternating Current (AC)
A voltage that changes its polarity and magnitude at regular intervals of time is
called an ‘alternating voltage’ or sometimes AC voltage.
The current flowing in a circuit with AC voltage supply is also alternating in
nature, and is known as alternating current.
An AC voltage can be produced by a generator, called an alternator.
In the simplified generator shown, the conductor loop rotates through the mag-
netic field and cuts lines of force to generate an induced ac voltage across its
terminals.
Commercial alternators produce sinusoidal alternating voltage i.e. alternating
voltage is a sine wave.
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3. A Simple AC Generator
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4. Remarks & Important Terms
The sinusoidal alternating voltage can be expressed by the equation :
v = Vm sinθ
v = Vm sinωt
Where,
v = Instantaneous value of alternating voltage
Vm = Max. value of alternating voltage
ω = Angular velocity of the coil
Since, the nature of cosine function is also same, hence an AC voltage can
also be represented as v = Vm sinωt
AC quantities are represented graphically by a wave shape or wave form. We
are concerned only with sinusoidal waveforms. However, AC can also be of
triangular, square etc. shape.
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5. Remarks & Important Terms...Contd
Cycle: One complete set of positive and negative values of an alternating
quantity is known as a cycle.
Time Period: The time taken in seconds to complete one cycle of an alternat-
ing quantity is called its time period. It is generally represented by T.
Frequency: The number of cycles that occur in one second is called the fre-
quency ( f) of the alternating quantity. It is measured in cycles/sec (C/s) or
Hertz (Hz). One Hertz is equal to 1 C/s.
Frequency and Time period are reciprocal of each other i. e. f =
1
T
Supply frequency in India is 50 Hz.
Relation between frequency and angular velocity: ω = 2π f rad/s
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6. Illustration of various terms
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7. Illustration...Contd
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8. Various values associated with an AC quantity
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9. Various values associated with an AC quantity
1. Max. value/Peak value/Amplitude: The maximum value attained by an al-
ternating quantity during one cycle is called ‘peak value’. This is also called
‘maximum value or crest value or amplitude’. Denoted by Vm or Im
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10. Various values associated with an AC quantity
1. Max. value/Peak value/Amplitude: The maximum value attained by an al-
ternating quantity during one cycle is called ‘peak value’. This is also called
‘maximum value or crest value or amplitude’. Denoted by Vm or Im
2. Average value: The arithmetic average of all the instantaneous values con-
sidered over one cycle of an alternating quantity (current or voltage) is called
its average value. In case of symmetrical waves (such as sinusoidal current or
voltage wave), the positive half is exactly equal to the negative half; therefore,
the average value over a complete cycle is zero. The half-cycle average value
is given by: Vav =
2
π
Vm = 0.637Vm
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11. Various values associated with an AC quantity
1. Max. value/Peak value/Amplitude: The maximum value attained by an al-
ternating quantity during one cycle is called ‘peak value’. This is also called
‘maximum value or crest value or amplitude’. Denoted by Vm or Im
2. Average value: The arithmetic average of all the instantaneous values con-
sidered over one cycle of an alternating quantity (current or voltage) is called
its average value. In case of symmetrical waves (such as sinusoidal current or
voltage wave), the positive half is exactly equal to the negative half; therefore,
the average value over a complete cycle is zero. The half-cycle average value
is given by: Vav =
2
π
Vm = 0.637Vm
3. RMS value: Also known as effective value. Its definition is based on the heat-
ing effect of current. It is given by: IRMS =
Im
√
2
= 0.707Im
Residential Supply voltage in India is 230 V (RMS).
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12. AC Circuit with Resistance
i = Im sinωt
=
Vm
R
sinωt
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13. AC Circuit with Resistance...Contd
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14. AC Circuit with Resistance...Contd
When AC voltage is supplied to a resistor, the resulting current is also AC.
Further, the current waveform starts simultaneously with the voltage waveform
Thus, it can be said that the voltage and current in a purely resistive circuit are
In Phase
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15. AC Circuit with Inductance
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16. AC Circuit with Inductance...Contd
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17. AC Circuit with Inductance...Contd
In a purely inductive circuit connected to AC supply, the current lags behind the
voltage by 90◦.
We know that an EMF is induced in the inductor due to self induction, but it is
of opposite polarity to the supply voltage due to Lenz’s law.
Hence, we can write eself = −v. But e = L
∆i
∆t
. Therefore, v = L
∆i
∆t
Now, let us analyze the situation in terms of slope of the current waveform.
Initially, current starts from negative peak value, but the slope here is zero,
hence voltage is zero.
As time increases, the slope also increases and becomes maximum at the
instant when current crosses the time axis.
At this instant, the voltage has reached its maximum value. It can be seen that
the voltage has a sine waveform while current has a negative cosine waveform.
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18. AC Circuit with Inductance...Contd
This means that the phase difference between voltage and current is 90◦.
Since, current reaches its respective values after 90◦that of voltage and we say
that it lags voltage by 90◦. Voltage and current equations are then written as:
v = Vm sin(ωt)
i = −Im cos(ωt) = Im sin(ωt −90◦
)
See further: AC Inductor Circuits
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19. AC Circuit with Capacitance
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20. AC Circuit with Capacitance
See Yourself
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21. AC Circuit with Capacitance
See Yourself
v = Vm sin(ωt)
i = Im cos(ωt) = Im sin(ωt +90◦
)
See further: AC Capacitor Circuits
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