AC circuits: inductive reactance, capacitive reactance, impedance and admittance
• voltage-current profiles of L, C, RL, RC and circuits
• impedance of RL, RC and RLC circuits
Notes from Gibilisco; Teach
Yourself Electricity and
Electronics, McGraw-Hill,
Chapters 13-15
CHM6158C - Lecture 18
1

Inductive reactance (X
L
) inductance = property of circuit where change in electric current through the circuit induces an electromotive force that opposes the change in current
= …..
Inductive reactance:
Increase AC frequency – what will be the effect?
Frequency (Hz)
Inductance
(Henrys =
Ω s)
X
L
6 .
28 fL
2

Examples
• inductance = 0.50 H, frequency = 60 Hz, what is X
L
?
• for the same circuit as above, we use a battery with 12 VDC, what is X
L
?
What are the units of X
L
?
3

Voltage-current profile
For pure inductance circuit For pure resistance circuit
Current lags driving (source) voltage Current in phase with driving (source) voltage
4

Inductive reactance and resistance
5

Combined inductance and resistance
6

Phase angle
Apply Pythagoras to obtain hypotenuse = impedance sin
φ
=
7

Capacitive reactance (X
C
)
Similarly to inductance, capacitance has an effect on impedance
By convention, capacitive reactance is expressed as a negative ohmic value
8

AC and capacitance
What is the voltage-current profile going to look like?
9

Current leads voltage
Hz
F
Capacitive reactance:
X
C
1 /( 6 .
28 fC )
10

Inverse relationship
Intuitive understanding:
Larger C
⇒ more movement of charge
⇒ smaller resistance
Higher f
⇒ more movement of charge
⇒ approach short-circuit
11

Examples
• capacitor = 0.001
μ
F, frequency = 1 MHz, what is X
C
?
• for the same circuit as above, we use a battery with 12 VDC, what is X
C
?
For the second question, what this mean for transmission on
DC across a capacitor?
12

Combined capacitive reactance and resistance
Work out phase angle
13

Impedance
Impedance (Z) = resistance to AC current, composed of resistance, inductive reactance and capacitive reactance
Inductive reactance
Absolute value of impedance
Resistance
Capacitive reactance
14

RLC in-series circuit
Z = R + j(X
L
+ X
C
)
Examples:
• R = 50
Ω
, X
L
= 22
Ω
, X
C
= -33
Ω
• R = 50
Ω
, X
L
= 444
Ω
, X
C
= -444
Ω
15

Inverse definitions
DC circuit
Resistance ( R )
≠ conductance ( G )
AC circuit
Impedance ( Z )
≠ admittance ( Y )
Reactance ( X )
≠ susceptance ( B )
BUT , note sign inversion for imaginary numbers:
B
C
= 1/X
C numbers:
, but due to imaginary jB
C
= -j/X
C
Example:
X
C
= 10
Ω
, what is jB
C
?
jB
C
= 1/(j10) = (1/j)(1/10) = -j 0.1
16

RLC in-parallel
Y = G + j(B
L
+ B
C
)
Example:
• G = 0.1 Siemens, B
L
B
C
= j0.020
= -j0.010,
GB plane
17