LECTURE 7: AC Circuit Analysis:
AC ANALYSIS
Instructor:
Mr. L Tivani
Contact: ltivani@uj.ac.za
Office Hours:
LAB 2 Room 103
Blackboard course name:
Electrotechnics ETN1B21
AC ANALYSIS
Objectives:
 Compute impedance, addition, subtraction, multiplication and division of
complex numbers, and power triangle involving capacitors and inductors.
AC Analysis
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Addition and Subtraction of Complex Numbers This is
easiest to perform in rectangular form.
Multiplication and Division of Complex Numbers This is easiest to
perform in polar form.
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sin
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In an A.C. circuit containing resistance R, the
applied voltage V is in phase with VR
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In an A.C. circuit containing inductance L and
resistance R, the applied voltage V is the phasor
sum of VR and VL
Z L  jw L
YL  1
j

jw L w L
The phasor transform of an inductor is an inductor with an
impedance of jwL. In other words, the inductor has an impedance in
the phasor domain which increases with frequency. This comes from
taking the ratio of phasor voltage to phasor current for an inductor, and
is a direct result of the inductor voltage being proportional to the
derivative of the current. For an inductor, the impedance and
admittance are purely imaginary. The impedance has a positive
imaginary part, and the admittance has a negative imaginary part.
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In an AC series circuit containing capacitance C
and resistance R, the applied voltage V is the
phasor sum of VR and VC
1
j
ZC 

YC  jw C
jwC
wC
The phasor transform of a capacitor is a capacitor with an admittance
of jwC. In other words, the capacitor has an admittance in the phasor
domain which increases with frequency. This comes from taking the
ratio of phasor current to phasor voltage for a capacitor, and is a direct
result of the capacitive current being proportional to the derivative of
the voltage. For a capacitor, the impedance and admittance are purely
imaginary. The impedance has a negative imaginary part, and the
admittance has a positive imaginary part.
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In an AC series circuit containing resistance R,
inductance L and capacitance C, the applied
voltage V is the phasor sum of VR, VL and VC
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The impedance and the admittance for a combination of
elements will be complex. Thus, the impedance, or the
admittance, can have a real part and an imaginary part.
Alternatively, we can think of these values as having
magnitude and phase. We have names for the real and
imaginary parts. These names are shown below.
Z X  R + jX
YX  G + jB
Reactance
Impedance
Resistance
Susceptance
Admittance
Conductance
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