20'5 Energy stored in magnetic fields'

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20.5 Energy stored in magnetic fields.
Energy stored in an inductor Energy stored in
the magnetic field
2
Energy is stored in an inductor The energy is
stored in the magnetic field
B
B0
?Vs
L
I0
Switch
After the current flows a B field builds up in
the inductor. Work is done to increase the
current from I0, to I
3
Work is done to increase the current against the
induced emf.
changing current
e
I
I?I
?work not constant but depends on I need to sum
(integral in calculus) ?W
4
Total work depends on the sum of incremental work
W
?I
I
potential energy due to I
5
A coil with L10-3 H carries a current of 10 A.
How much potential energy is stored in the
inductor?
6
Energy Stored in the magnetic field for a long
solenoid
B
The energy density ?B (energy/volume) just
depends on B2
7
The magnetic field at the earths surface has a
magnitude of 0.5 x10-4T. Find the magnetic field
energy in a volume of 1m3.
8
Energy is stored in a magnetic fields
(inductor) Energy is stored in electric
fields (capacitor) This energy will be
important when we consider electromagnetic
radiation where energy is transferred in the
form of electric and magnetic fields.
B
E
9
21.1 Alternating current circuits

• Resistors, capacitors and inductors in an ac
  circuit.
• Average properties. Voltage, current, power
• The quiz will only cover chapter 20.

10
Household electricity comes as an alternating
current (ac). We discuss the different
behavior of resistors, capacitors and inductors
in ac circuits.
11
Resistor in an AC circuit
IImaxsin2pft
?v?vmaxsin2pft
In phase- Imax and vmax occur at the same time
Imax
T
vmax
T period
t
Frequency cycle/s (Hz)
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Imax
vmax
0
t
Average of I and average of V 0
Equally likely to have and values.
13
The power dissipation depend on V2, and I2.
This is because dissipation occurs regardless of
the direction of the current.
The average of ?V2 and I2 are important for
power.
The average of ?V2 and I2 are not zero.
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Root mean square, RMS ?V
square root of the average of ?V2
?Vmax
RMS ?V
?V
0
t
Average?V2
0
?V2
t
?VRMS
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Similarly
The average power is then
Generally when we refer to ac voltage, current or
power these are the RMS values
16
An ac voltage has an RMS voltage of 120V. a) Find
the maximum voltage. b) Find the peak power
through a 10O resistor.