Download AC circuits: inductive reactance, capacitive reactance, impedance

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 (XL)
inductance = property of circuit where change in electric current through the
circuit induces an electromotive force that opposes the change in current
= …..
Increase AC frequency –
what will be the effect?
Frequency (Hz)
Inductive reactance:
Inductance
(Henrys = Ωs)
X L = 6.28 fL
2
Examples
• inductance = 0.50 H, frequency = 60 Hz, what is XL?
• for the same circuit as above, we use a battery with 12 VDC, what is XL?
What are the units of XL?
3
Voltage-current profile
For pure inductance circuit
Current lags driving (source) voltage
For pure resistance circuit
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
sinφ =
7
Capacitive reactance (XC)
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
Capacitive reactance:
F
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 μF, frequency = 1 MHz, what is XC?
• for the same circuit as above, we use a battery with 12 VDC, what is XC?
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(XL + XC)
Examples:
• R = 50 Ω, XL = 22 Ω, XC = -33 Ω
• R = 50 Ω, XL = 444 Ω, XC = -444 Ω
15
Inverse definitions
DC circuit
AC circuit
Resistance (R) ≠ conductance (G)
Impedance (Z) ≠ admittance (Y)
Reactance (X) ≠ susceptance (B)
BUT, note sign inversion for
imaginary numbers:
BC = 1/XC, but due to imaginary
numbers:
jBC = -j/XC
Example:
XC = 10 Ω, what is jBC?
jBC = 1/(j10) = (1/j)(1/10) = -j 0.1
16
RLC in-parallel
Y = G + j(BL + BC)
GB plane
Example:
• G = 0.1 Siemens, BL = -j0.010,
BC = j0.020
17