Finish Chapter 27: Electromagnetic Induction Chapter 28 ...shill/Teaching/2049...
Transcript of Finish Chapter 27: Electromagnetic Induction Chapter 28 ...shill/Teaching/2049...
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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)
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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
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LR circuits (similarity to RC circuit)
I = !0R1" e"Rt /L( )
! = LR
Time constant:
R
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LR circuits (similarity to RC circuit)
!L = !!0e!Rt/L = !!0e
! t/"
! = LR
Time constant:
R
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LR circuits (similarity to RC circuit)
!L = !!0e!Rt/L = !!0e
! t/"
! = LR
Time constant:
t = ! !L = 0
R
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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.
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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
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Ch. 28: Electromagnetic oscillations
U =UB+U
E=12LI 2 +
12Q2
C
Q(t) =Qm
cos!t
I(t) =!!Qm
sin!t
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U =UB+U
E=12LI 2 +
12Q2
C! =
1LC
Ch. 28: Electromagnetic oscillations
Q(t) =Qm
cos!t
I(t) =!!Qm
sin!t
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Qm2
2C= 1
2LI
m2
U =UB+U
E=12LI 2 +
12Q2
C
Ch. 28: Electromagnetic oscillations
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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: