Finish Chapter 27: Electromagnetic Induction Chapter 28: Alternating-Current Circuits

Tuesday November 1st

• Review of Inductors • Review of RL Circuits • Energy and oscillations in LC circuits • Intro to alternating current theory

• Defn of terms, e.g., rms values • Resistance • Capacitive reactance • Inductive reactance

Reading: up to page 498 in the text book (Ch. 28)

• Mini-exam 4 on Thursday •  Will cover Ch. 26 & 27 (LONCAPA 13-16)

Review: Inductors

• We can, therefore, define a quantity L called inductance, which relates I to ΦB and, thus, dI/dt and ε:

!L=!L

dIdt

dIdt !

L

I

!B= LI

Units for L: weber/amp T.m2/A Henry (H)

B = µonISolenoid:

L = µon2Al

LR circuits (similarity to RC circuit)

I = !0R1" e"Rt /L( )

! = LR

Time constant:

R

LR circuits (similarity to RC circuit)

!L = !!0e!Rt/L = !!0e

! t/"

! = LR

Time constant:

R

LR circuits (similarity to RC circuit)

!L = !!0e!Rt/L = !!0e

! t/"

! = LR

Time constant:

t = ! !L = 0

R

Example

A 3.5 V battery is connected in series with a switch, a resistor and an inductor. The switch is thrown at time t = 0. The current reaches half its maximum value after 1.2 ms. After a long time, the current reaches a maximum of 255 mA. Deduce values for the resistance and inductance in the circuit.

Energy Stored in an Inductor

!L-IR

Close switch at time t = 0

UL = 12 LI

2

Energy stored in magnetic fields:

Energy density: uB =Energy

unit volume= B2

2µo

Ch. 28: Electromagnetic oscillations

U =UB+U

E=12LI 2 +

12Q2

C

Q(t) =Qm

cos!t

I(t) =!!Qm

sin!t

U =UB+U

E=12LI 2 +

12Q2

C! =

1LC

Ch. 28: Electromagnetic oscillations

Q(t) =Qm

cos!t

I(t) =!!Qm

sin!t

Qm2

2C= 1

2LI

m2

U =UB+U

E=12LI 2 +

12Q2

C

Ch. 28: Electromagnetic oscillations

Ch. 28: Alternating Current V(t)=V

Psin !t +!

V( ); I(t)= IP sin !t +!I( )

Sine curve starts at ωt = -π/6 or -30o

In this example: ϕV = +π/6 or 30o

Root-Mean-Square:

Vrms

=V

P

2

Irms

=I

P

2

! = 2!fAngular frequency: