Transcript
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 1/66
Copyright © 2012 Pearson Education Inc.
PowerPoint® Lectures for
Univers i ty Physics , Thir teenth Edit io n
– Hugh D. Young and Roger A. Freedman
Lectures by Wayne Anderson
Chapter 30
Inductance
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 2/66
Copyright © 2012 Pearson Education Inc.
Energy through space for free??
• A puzzler!
Increasing
current in
time
Creates
increasing flux
INTO ring
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 3/66
Copyright © 2012 Pearson Education Inc.
Energy through space for free??
• A puzzler!
Increasing
current in
time
Creates
increasing flux
INTO ring
Induce
counter-clockwise
current and
B field OUT
of ring
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 4/66
Copyright © 2012 Pearson Education Inc.
Energy through space for free??
• But… If wire loop has resistance R, current
around it generates energy! Power = i2
/R!!
Increasing
current in
time
Induced currenti around loop of
resistance R
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 5/66
Copyright © 2012 Pearson Education Inc.
Energy through space for free??
• Yet…. NO “potential difference”!
Increasing
current in
timeInduced current
i around loop ofresistance R
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 6/66
Copyright © 2012 Pearson Education Inc.
Energy through space for free??
• Answer? Energy in B field!!
Increasing
current in
time
Increased fluxinduces EMF in
coil radiating
power
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 7/66Copyright © 2012 Pearson Education Inc.
Goals for Chapter 30 - Inductance
• To learn how current in one coil can induce anemf in another unconnected coil
• To relate the induced emf to the rate of changeof the current
• To calculate the energy in a magnetic field
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 8/66Copyright © 2012 Pearson Education Inc.
Goals for Chapter 30
• Introduce circuit components calledINDUCTORS
• Analyze circuits containing resistors and
inductors
• Describe electrical oscillations in circuits and
why the oscillations decay
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 9/66Copyright © 2012 Pearson Education Inc.
Introduction
• How does a coil induce a
current in a neighboring coil.
• A sensor triggers the traffic
light to change when a car
arrives at an intersection. How
does it do this?
• Why does a coil of metal
behave very differently from a
straight wire of the same metal?
• We’ll learn how circuits can be
coupled without being
connected together.
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 10/66Copyright © 2012 Pearson Education Inc.
Mutual inductance
• Mutual inductance: A changing current in one coil
induces a current in a neighboring coil.
Increase current
in coil 1
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 11/66Copyright © 2012 Pearson Education Inc.
Mutual inductance
• Mutual inductance: A changing current in one coil
induces a current in a neighboring coil.
Increase current
in coil 1
Increase B flux
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 12/66Copyright © 2012 Pearson Education Inc.
Mutual inductance
• Mutual inductance: A changing current in one coil
induces a current in a neighboring coil.
Increase current
in coil 1
Increase B flux
Induce current in
loop 2
Induce fluxopposing change
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 13/66Copyright © 2012 Pearson Education Inc.
Mutual inductance
• EMF induced in single loop 2 = - d (B2 )/dt
– Caused by change in flux through second loop of B field
– Created by the current in the single loop 1
• So… B2 is proportional to i1
• What does that proportionality constant depend upon?
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 14/66
Copyright © 2012 Pearson Education Inc.
Mutual inductance
• B2 is proportional to i1 and is affected by:
– # of windings in loop 1
– Area of loop 1
– Area of loop 2
• Define “M” as mutual inductance of coil 1 on coil 2
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 15/66
Copyright © 2012 Pearson Education Inc.
Mutual inductance
• Define “M” as mutual inductance on coil 2 from coil 1
• B2 = M21 I
• But what i f loop 2 also has many turns?
Increase #turns in
loop 2? =>
increase flux!
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 16/66
Copyright © 2012 Pearson Education Inc.
Mutual inductance
• IF you have N turns in
coil 2,
each with flux B ,
total flux is Nx larger
• Total Flux = N2 B2
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 17/66
Copyright © 2012 Pearson Education Inc.
Mutual inductance
• B2 proportional to i1
So
N2
B
= M21
i1
M 21 is the “Mutual Inductance”
[Units] = Henrys = Wb/Amp
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 18/66
Copyright © 2012 Pearson Education Inc.
Mutual inductance
• EMF2 = - N2 d [B2 ]/dt
and
• N2 B = M21i1
so
• EMF2 = - M21d [i1]/dt
• Because geometry is
“shared” M21 = M12 = M
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 19/66
Copyright © 2012 Pearson Education Inc.
Mutual inductance
• Define Mutual inductance:
A changing current in one
coil induces a current in a
neighboring coil.
• M = N2 B2/i1
M = N1 B1/i2
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 20/66
Copyright © 2012 Pearson Education Inc.
Mutual inductance examples
• Long solenoid with length l, area A, wound with N1 turns of wire
•
N2 turns surround at its center. What is M?
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 21/66
Copyright © 2012 Pearson Education Inc.
Mutual inductance examples
• M = N2 B2/i1
•
We need B2 from the first solenoid (B1 = m oni1 )
• n = N 1 /l
• B2 = B1 A
• M = N2 m oi1 A N 1 /l i1
• M = m oA N 1 N2 /l
• All geometry!
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 22/66
Copyright © 2012 Pearson Education Inc.
Mutual inductance examples
• M = m oA N 1 N2 /l
•
If N 1 = 1000 turns, N 2 = 10 turns, A = 10 cm2
, l = 0.50 m – M = 25 x 10-6 Wb/A
– M = 25 m H
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 23/66
Copyright © 2012 Pearson Education Inc.
Mutual inductance examples
• Using same system ( M = 25 m H)
•
Suppose i2 varies with time as = (2.0 x 106
A/s)t
• At t = 3.0 ms, what is average flux through each turn of coil 1?
• What is induced EMF in solenoid?
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 24/66
Copyright © 2012 Pearson Education Inc.
Mutual inductance examples
• Suppose i2 varies with time as = (2.0 x 106 A/s)t
•
At t = 3.0 ms, i2 = 6.0 Amps
• M = N1 B1/i2 = 25 m H
• B1= Mi2/N1 = 1.5x10-7 Wb
• Induced EMF in solenoid?
– EMF1 = -M(di2/dt)
– -50Volts
S lf i d
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 25/66
Copyright © 2012 Pearson Education Inc.
Self-inductance
• Self-inductance: A varying current in a circuit induces an emf
in that same cir cuit.
• Always opposes the change!
• Define L = N B/i
•
Li = N B
• I f i changes in time:
• d(L i)/dt = Nd B /dt = -EMF
or
• EMF = -Ldi/dt
I d i i l !
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 26/66
Copyright © 2012 Pearson Education Inc.
Inductors as circuit elements!
• Inductors ALWAYS oppose change:
• In DC circuits:
– Inductors maintain steady current flow
even if supply varies
• In AC circuits:
– Inductors suppress (filter) frequencies
that are too fast.
P t ti l i d t
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 27/66
Copyright © 2012 Pearson Education Inc.
Potential across an inductor
•
The potential across aninductor depends on the
rate of change of the
current through it.
• The self-induced emf
does not oppose current,
but opposes a change in
the current.
V ab = -Ld i/dt
M ti fi ld
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 28/66
Copyright © 2012 Pearson Education Inc.
Magnetic field energy
• Inductors store energy in the magnetic field:
U = 1/2 LI 2
• Units: L = Henrys (from L = N B/i )
• N B/i = B-field Flux/current through inductor that
creates that fluxWb/Amp = Tesla-m2/Amp
• [U] = [Henrys] x [Amps]2
• [U] = [Tesla-m2/Amp] x [Amps]2 = Tm2Amp
• But F = qv x B gives us definition of Tesla
• [B] = Teslas= Force/Coulomb-m/s = Force/Amp-m
M ti fi ld
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 29/66
Copyright © 2012 Pearson Education Inc.
Magnetic field energy
• Inductors store energy in the magnetic field:
U = 1/2 LI 2
• [U] = [Tesla-m2/Amp] x [Amps]2 = Tm2Amp
• [U] = [Newtons/Amp-m] m2Amp
= Newton-meters = Joules = Energy!
M ti fi ld
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 30/66
Copyright © 2012 Pearson Education Inc.
Magnetic field energy
• The energy stored in an inductor is U = 1/2 LI 2.
• The energy density in a magnetic field (Joule/m3) is
• u = B2/2m0 (in vacuum)
• u = B2/2m (in a magnetic material)
• Recall definition of m0 (magnetic permeability)
• B = m0 i/2pr (for the field of a long wire)
• m0 = Tesla-m/Amp
• [u] = [B2/2m0] = T2/(Tm/Amp) = T-Amp/meter
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 31/66
C l l ti lf i d t d lf i d d f
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 32/66
Copyright © 2012 Pearson Education Inc.
Calculating self-inductance and self-induced emf
• Toroidal solenoid with area A, average radius r, N turns.
• Assume B is uniform across cross section. What is L?
Calculating self inductance and self induced emf
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 33/66
Copyright © 2012 Pearson Education Inc.
Calculating self-inductance and self-induced emf
• Toroidal solenoid with area A, average radius r, N turns.
•
L = N B/i
• B = BA = (mo Ni/2pr)A
• L = mo N2A/2pr (self inductance of toroidal solenoid)
• Why N 2 ??
• If N =200 Turns, A = 5.0 cm2,
r = 0.10 m
L = 40 mH
Potential across an inductor
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 34/66
Copyright © 2012 Pearson Education Inc.
Potential across an inductor
• The potential across a
resistor drops in the
direction of current flow
Vab = Va-V b > 0
• The potential across an
inductor depends on the
rate of change of the
current through it.
Potential across an inductor
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 35/66
Copyright © 2012 Pearson Education Inc.
Potential across an inductor
• The potential across an
inductor depends on the
rate of change of the
current through it.
• The self-induced emf
does not oppose current, but opposes a change in
the current.
Potential across an inductor
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 36/66
Copyright © 2012 Pearson Education Inc.
Potential across an inductor
• The potential across an
inductor depends on the
rate of change of the
current through it.
• The self-induced emf does
not oppose current, butopposes a change in the
current.
• The inductor acts like atemporary voltage source
pointing OPPOSITE to the
change.
Potential across an inductor
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 37/66
Copyright © 2012 Pearson Education Inc.
Potential across an inductor
•
The inductor acts like atemporary voltage source
pointing OPPOSITE to the
change.
• This implies the inductor
looks like a battery
pointing the other way!
• Note Va > V b!
Direction of current flow
from a battery oriented
this way
Potential across an inductor
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 38/66
Copyright © 2012 Pearson Education Inc.
Potential across an inductor
• What if current was
decreasing?
• Same result! The inductor
acts like a temporary voltage
source pointing OPPOSITE
to the change.
• Now inductor pushes current
in original direction
• Note Va < V b!
The R L circuit
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 39/66
Copyright © 2012 Pearson Education Inc.
The R-L circuit
• An R-L circuit contains aresistor and inductor and
possibly an emf source.
• Start with both switches open
• Close Switch S1:
• Current flows
• Inductor resists flow
• Actual current less thanmaximum E/R
• E – i(t)R- L(di/dt) = 0
• di/dt = E /L – (R/L)i(t)
The R L circuit
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 40/66
Copyright © 2012 Pearson Education Inc.
The R-L circuit
• Close Switch S1:
• E
–
i(t)R- L(di/dt) = 0• di/dt = E /L – (R/L)i(t)
Boundary Conditions
• At t=0, di/dt = E /L
• i( ) = E /R
Solve this 1 st order diff eq:
• i(t) = E /R (1-e -(R/L)t )
Current growth in an R-L circuit
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 41/66
Copyright © 2012 Pearson Education Inc.
Current growth in an R-L circuit
• i(t) = E /R (1-e -(R/L)t )
• The time constant for an R-L circuit is = L/R.
• [ ]= L/R = Henrys /Ohm
• = (Tesla-m2/Amp)/Ohm
• = ( Newtons/Amp-m) (m2/Amp)/Ohm
• = (Newton-meter) / (Amp2-Ohm)
• = Joule/Watt
• = Joule/(Joule/sec)
• = seconds!
Current growth in an R-L circuit
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 42/66
Copyright © 2012 Pearson Education Inc.
Current growth in an R-L circuit
• i(t) = E /R (1-e -(R/L)t )
• The time constant for an R-L circuit is = L/R.
• [ ]= L/R = Henrys /Ohm
• EMF = -Ldi/dt
• [L] = Henrys = Volts /Amps/sec
• Volts/Amps = Ohms (From V = IR)
• Henrys = Ohm-seconds
• [ ]= L/R = Henrys /Ohm = seconds!
V ab = -Ld i/dt
The R-L circuit
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 43/66
Copyright © 2012 Pearson Education Inc.
The R-L circuit
• E = i(t)R+ L(di/dt)
• Power in circuit = E I
• E i = i2 R+ Li(di/dt)
• Some power radiated in resistor
• Some power stored in inductor
The R-L circuit example
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 44/66
Copyright © 2012 Pearson Education Inc.
The R L circuit example
• R = 175 W ; i = 36 mA; currentlimited to 4.9 mA in first 58 m s.
• What is required EMF
• What is required inductor
• What is the time constant?
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 45/66
Current decay in an R-L circuit
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 46/66
Copyright © 2012 Pearson Education Inc.
Current decay in an R L circuit
• Now close the secondswitch!
• Current decrease is opposed by inductor
• EMF is generated to keep
current flowing in the samedirection
• Current doesn’t drop to zeroimmediately
Current decay in an R-L circuit
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 47/66
Copyright © 2012 Pearson Education Inc.
Current decay in an R L circuit
• Now close the secondswitch!
• – i(t)R - L(di/dt) = 0
• Note di/dt is NEGATIVE!
• i(t) = -L/R(di/dt)
• i(t) = i(0)e -(R/L)t
• i(0) = max current before
second switch is closed
Current decay in an R-L circuit
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 48/66
Copyright © 2012 Pearson Education Inc.
Current decay in an R L circuit
• i(t) = i(0)e -(R/L)t
Current decay in an R-L circuit
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 49/66
Copyright © 2012 Pearson Education Inc.
Current decay in an R L circuit
• Test yourself!
• Signs of Vab and Vbc whenS1 is closed?
• Vab >0; Vbc >0
• Vab >0, Vbc <0• Vab <0, Vbc >0
• Vab <0, Vbc <0
Current decay in an R-L circuit
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 50/66
Copyright © 2012 Pearson Education Inc.
Current decay in an R L circuit
• Test yourself!
• Signs of Vab and Vbc whenS1 is closed?
• Vab >0; Vbc >0
• Vab >0, Vbc <0• Vab <0, Vbc >0
• Vab <0, Vbc <0
• WHY?
• Current increases suddenly, so inductorresists change
Current decay in an R-L circuit
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 51/66
Copyright © 2012 Pearson Education Inc.
Current decay in an R L circuit
• Test yourself!
• Signs of Vab and Vbc whenS1 is closed?
• Vab >0; Vbc >0
• WHY?• Current still flows
around the circuitcounterclockwise
through resistor• EMF generated in L is
from c to b
• So Vb> Vc!
Current decay in an R-L circuit
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 52/66
Copyright © 2012 Pearson Education Inc.
Cu e dec y c cu
• Test yourself!
• Signs of Vab and Vbc whenS2 is closed, S1 open?
• Vab >0; Vbc >0
• Vab >0, Vbc <0• Vab <0, Vbc >0
• Vab <0, Vbc <0
Current decay in an R-L circuit
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 53/66
Copyright © 2012 Pearson Education Inc.
y
• Test yourself!
• Signs of Vab and Vbc whenS2 is closed, S1 open?
• Vab >0; Vbc >0
• Vab >0, Vbc <0
• WHY?
• Current still flowscounterclockwise
• di/dt <0; EMF generated in Lis from b to c!So Vb < Vc!
The L-C circuit
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 54/66
Copyright © 2012 Pearson Education Inc.
• An L-C circuit contains an inductor and a capacitor and is anoscillating circuit.
• Initially capacitor fully charged; close switch
• Charge flows FROM capacitor, but inductorresists that increased flow.
• Current builds in time.
• At maximum current, charge flow nowdecreases through inductor
• Inductor now resists decreased flow, andkeeps pushing charge in the original direction
i
The L-C circuit
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 55/66
Copyright © 2012 Pearson Education Inc.
• An L-C circuit contains an inductor and a capacitor and is anoscillating circuit.
• Initially capacitor fully charged; close switch
• Charge flows FROM capacitor, but inductorresists that increased flow.
• Current builds in time.
• Capacitor slowly discharges
• At maximum current, no charge is left on
capacitor; current now decreases throughinductor
• Inductor now resists decreased flow, andkeeps pushing charge in the original direction
i
The L-C circuit
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 56/66
Copyright © 2012 Pearson Education Inc.
• An L-C circuit contains an inductor and a capacitor and is anoscillating circuit.
The L-C circuit
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 57/66
Copyright © 2012 Pearson Education Inc.
• An L-C circuit contains an inductor and a capacitor and is anoscillating circuit.
• Now capacitor fully drained;
• Inductor keeps pushing charge in theoriginal direction
• Capacitor charge builds up on other sideto a maximum value
• While that side charges, “back EMF” from
capacitor tries to slow charge build-up
• Inductor keeps pushing to resist that change.
i
The L-C circuit
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 58/66
Copyright © 2012 Pearson Education Inc.
• An L-C circuit contains an inductor and a capacitor and is anoscillating circuit.
The L-C circuit
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 59/66
Copyright © 2012 Pearson Education Inc.
• An L-C circuit contains an inductor and a capacitor and is anoscillating circuit.
• Now capacitor charged on opposite side;
• Current reverses direction! System repeatsin the opposite direction
i
The L-C circuit
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 60/66
Copyright © 2012 Pearson Education Inc.
• An L-C circuit contains an inductor and a capacitor and is anoscillating circuit.
Electrical oscillations in an L-C circuit
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 61/66
Copyright © 2012 Pearson Education Inc.
• Analyze the current and
charge as a function of time.
• Do a Kirchoff Loop around
the circuit in the direction
shown.
• Remember i can be +/-
• Recall C = q/V
• For this loop:
-Ldi/dt – qC = 0
Electrical oscillations in an L-C circuit
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 62/66
Copyright © 2012 Pearson Education Inc.
• -Ldi/dt – qC = 0
• i(t) = dq/dt
• Ld 2q/dt 2 + qC = 0
• Simple Harmonic Motion!
• Pendulums
• Springs
• Standard solution!
• q(t)= Qmax cos( w t+f )
where w = 1/(LC)½
Electrical oscillations in an L-C circuit
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 63/66
Copyright © 2012 Pearson Education Inc.
• q(t)= Qmax cos( w t+f )
• i(t) = - w Qmax sin( w t+f )
(based on this ASSUMED
direction!!)
• w = 1/(LC)½ =
angular frequency
The L-C circuit
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 64/66
Copyright © 2012 Pearson Education Inc.
• An L-C circuit contains an inductor and a capacitor and is anoscillating circuit.
Electrical and mechanical oscillations
8/13/2019 30 Lecture Outline
http://slidepdf.com/reader/full/30-lecture-outline 65/66
Copyright © 2012 Pearson Education Inc.
• Table 30.1 summarizes the analogies between SHM and L-C
circuit oscillations.
The L-R-C series circuit
top related