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