Post on 13-Apr-2022
Chapter 28: Alternating-Current Circuits Tuesday November 8th
• Review of Mini Exam 4 • Review of LRC circuits
• Voltage/phase relations • Impedance • Resonance • Power in LRC circuits
• Example problem • Transformers • Maxwell’s equations (Ch. 29 – if time)
Reading: up to page 515 in the text book (Ch. 28/29)
Mini-exam 5 next Thursday (AC circuits and EM waves)
AC Circuits and R, L and C: a Summary
Capacitive reactance: XC
= 1/ !C (units - !)
Inductive reactance: XL= !L (units - !)
Phasor Diagrams: Adding the Voltages
tan! =
XL!X
C
R="L!1/ "C
R
V
p= I
pR2 + I
pX
L! I
pX
C( )2
! Ip=
Vp
R2 + XL!X
C( )2=Vp
Z
Z = R2 + X
L!X
C( )2
Modified Ohm’s law:
Impedance:
Phase:
Units:ohms!
"##
$
%&&
Resonance
Ip
=V
p
R2 + XL!X
C( )2
XL= X
C
XL> X
C
XL<X
C
V leads V lags
!
o=
1LC
At resonance, Z = R, and ϕ = 0 (just like a DC circuit)
tan! =XL!X
C
R
Resonance XL= X
C
XL> X
C
XL<X
C
V leads V lags
P = 1
2I
pV
pcos! = I
rmsV
rmscos!
Power delivered to the circuit:
Transformers
Soft iron
• Flux the same on both sides, but number of turns, N, is different • Total flux through primary and secondary coils depends on N1 and N2
V1= N
1!; V
2= N
2!; "
V2
V1
=N
2
N1
Transformers
Soft iron
• Energy must be conserved, so ‘power in’ must equal ‘power out’ • Therefor, I1V1 = I2V2
!
V2
V1
=I
1
I2
=N
2
N1