Lecture Slides for the course Fundamentals of Electrical Engineering delivered by me to First Semester Diploma in Mechanical Engineering.

1. PEE-102A
Fundamentals of Electrical Engineering
Lecture-6
Instructor:
Mohd. Umar Rehman
EES, University Polytechnic, AMU
April 3, 2021
PEE-102A U-II, L-6 April 3, 2021 1 / 10

2. Power in AC Circuits
As both voltage and current are alternating in AC circuits, hence power is also
alternating in nature in AC circuits.
In AC circuits, we are concerned with average power. It is also known as true
power, real power, active power.
In AC circuits, power also depends upon a factor known as power factor, which
determines the actual power consumption.
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3. Power in AC Circuit with Resistance...Contd
We know that for an AC circuit with resistance, the voltage and current can be
written as:
v = Vm sinθ, i = Im sinθ
Hence, power can be expressed as:
p = vi
= VmIm sin2
θ
= VmIm
1−cos2θ
2
=
VmIm
2
−
VmIm cos2θ
2
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4. Power in AC Circuit with Resistance...Contd
First term is constant and its average does not change, while the second term
is a term with frequency 2ω which has equal positive and negative values. thus
its average is zero.
Hence, the average power is given by:
Pav =
VmIm
2
=
Vm
√
2
Im
√
2
Pav = VrmsIrms
Pav = VI
The graphical variation is shown as follows.
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5. Power in an AC circuit with Resistance
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6. Power in an AC circuit with Inductance
We know that in an AC circuit with inductance,
v = Vm sinθ, i = −Im cosθ
Hence, power
p = vi
= −VmIm sinθ cosθ
= −
VmIm
2
sin2θ
Average power is zero. The waveforms are shown as follows.
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7. Power in an AC circuit with Inductance
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8. Power in an AC circuit with Inductance
In a similar way, average power in an AC circuit with capacitance is also zero.
See further: Power in AC Circuits
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9. Expression for Power in a general AC circuit
Consider an AC circuit in which a sinusoidal source supplies current to a gen-
eral load with inductive nature.
The voltage and current are given by:
v = Vm sinθ, i = Im sin(θ −φ)
where, φ is the phase difference between v i. Then, power is given by:
p = vi = VmIm sinθ sin(θ −φ)
=
VmIm
2
[cosφ −cos(2θ −φ)]
=
VmIm
2
cosφ −
VmIm
2
cos(2θ −φ)
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10. Expression for Power ...Contd
Taking the average of the above expression, we get
Pav =
VmIm
2
cosφ =
Vm
√
2
Im
√
2
cosφ
Pav = VrmsIrms cosφ
P = VI cosφ watts
The term cosφ is known as the power factor (PF). It is a measure of effective-
ness in utilizing the apparent power. It is defined in one of the following ways:
(a) PF = cosφ = cosine of phase angle difference between v i
(b) cosφ =
Average Power
Total Power
=
P
S
Value of PF for various circuits:
For R circuit, φ = 0◦ ⇒ cosφ = 1
For L circuit, φ = 90◦ ⇒ cosφ = 0
For C circuit, φ = 90◦ ⇒ cosφ = 0
In general, 0 PF 1
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11. Expression for Power ...Contd
The graphical variation is shown as follows.
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