inductance chapter 30 mutual inductance self-inductance magnetic-field energy r-l circuits l-c...
Post on 22-Dec-2015
229 views
TRANSCRIPT
Inductance Chapter 30• mutual inductance
• self-inductance
• magnetic-field energy
• R-L circuits
• L-C circuits
• L-R-C circuits
1
http://physci.kennesaw.edu/javamirror/CCP/21-5/CircuitiE.html
A straight wire has little inductance. Coil the wire an inductance increases.
A change in current in a coil induces an emf in an adjacent coil
Only time varying currents can induce and emf
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/indcur.html
Mutual InductancePotential induced in Coil-2
Flux in Coil-2 is proportional to the current in Coil-1, M12 is the mutual inductance
Assumed that magnetic material has a constant Km, so flux is directly proportional to current and M21 only depends on geometry
Even when the coils are not symmetric:
M=Henry= 1Wb/A
2
22 2
BdN
dt
2 2 12 1BN M i
2 12 21
Bd diN M
dt dt
12 21
diM
dt
12 21M M M
2 2 1 1
1 2
B BN NM
i i
Derivative with time
Mutual inductance—examples
3
M = mutual inductance is proportional to the of the turns N1N2
Self-inductance
4
5
Self-Inductance and Inductors
il
NKi
l
NB m 0
il
NAKBA mB 0 l
ANKL m
2
0
where L is the inductance in Henries
=
Liil
ANKN mB
2
0
Self-induced emf opposes changes in current• Self-inductance, L, depends upon on
size, shape, and turns, N• For N turns close together, L is
proportional to N2
• L depends upon magnetic material• If the core is not air, • For soft iron Km =5000 producing an L
5000 times greater than an air-core coil• Ferromagnetic material produce s L that
are not totally linear with current
6
0mK
7
Real Inductor is a combination of L and R
Vab
+
–
Ideal Inductor
+–Vab
Real Inductor
c
bcabac VVV
Ridt
diLVac
8
i
t
Inductor
Current and Voltage in an Inductive Circuit
Current can not change instantaneouslyvab
t
Inductor
i
t
vab
t
t0
t0
Inductor
Inductor
impossible
Theoretically the voltage can change instantaneously
9
Inductance (Chapter 30)Example 30-3 and 30-4 Calculating Self-Inductance and Induced EMF
Figure 30-8 Toroidal Solenoid
ir
NKi
r
NB m
22 0
ir
NAKBA mB
20
dt
diL
dt
di
r
ANK
dt
dNV m
BL
2
2
0
i
N
r
ANKL Bm
2
2
0
N = 200 turnsA = 5.0 cm2 = 5.0 x 10-4 m2
r = 0.1 m
i increases uniformly from 0 to 6.0 Ain 3.0 sec.
Determine L
Determine the magnitude anddirection of the induced emf ()
Km = 1
Inductance Application
– A charged coil can create a field that will induce a current in a neighboring coil.
– Inductance can allow a sensor to trigger the traffic light to change when the car arrives at an intersection. Circuit counts how many cars pass over the coil (how many changes in inductance).
– Bikes may not trigger circuit
– Drive back and forth in crease the car count?
10
11
Inductance (Chapter 30)The RL Circuit (30.4)
Figure 30-11
Figure 30-12 Increasing Current(S1 closed and S2 open)
Figure 30-13 Decreasing Current(S1 open and S2 closed)
0.37I0
0.63I
dt
diLVbc iRVab
dt
diLiRVV bcab
iL
R
LL
iR
dt
di
RLdt
di
t
0R
L
12
Details of current growth in an R-L circuit
0di
iR Ldt
iL
R
LL
iR
dt
di
Rdi i dt
L L
didt
Ri
L L
di Rdt
LiR
0
0 0
''
'
ln
ln ' | ' |
ln ln
ln
i t
o
i t
RtL
di Rdt
LiR
duu
uR
i tR L
Ri tR R L
i RR tL
R
iR e
R
Take exponent of both sides
13
1
RtL
RtL
RtL
RtL
iR e
R
i eR R
i eR R
i eR
L
R
Details of current growth in an R-L circuit -continued
0
RtLi e
R
IR
Decay current
R-L circuit current decay
Current thru L reaches I0 and S1 opens and S2 closes
14
0
RtLi e
R
IR
L-C oscillating circuit
• Consider Figure 30.14.
15
L-C Circuit
16
Mechanical Analog
17
Mechanical Analog L m mass1/C k spring constant
18
Inductance (Chapter 30)Energy Stored in an Inductor (30.3)
Figure 30-9
idt
diLiVp ab
pdtdw
i
o
t t
idiLdtdt
diLipdtw
0 0
dt
dwp
0
22
2
0
2 iL
iLw
i
2
2
1Liw joules
where w = energy stored in inductor i = current in inductor in amperes
(30.9)
L-R-C Circuit
19
20
21
22