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RL Circuits
Physics 102Professor Lee
CarknerLecture 22
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PAL #21 Generator
Set 180 V equal to the max emf = = /NBA = 180/(1)(2)(1) = 90 rad/s If = 90 rad/s, we can find f = /2 f =
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Induction and Circuits
The changing magnetic field can then induce a current
This means,
Note that induction only applies in circuits where the current changes often this means a switch is closed or opened
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Self Inductance
When the switch is closed, current flows through the loop, inducing a B field through the loop
Called self inductance
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Back emf
Works like a battery that is put in “backwards” Direction of emf depends on how current
changes
Current increases, emf in reverse direction Current decreases, emf in same direction
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Inductance and Increasing
Current
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Effect of Back emf
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Finding emf
emf depends on Faraday’s Law:
But the magnetic flux depends on the changing current and the properties of the coil
= -L(I/t)
where the constant of proportionality L is the inductance
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Inductance The unit of inductance is the henry,
The inductance of a circuit element (like a
solenoid) depends on the current and the flux flowing through it
L = N(/I)
Inductance is a property of the circuit element Like resistance
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Solenoid Inductance To find L, we need a relationship between and I
What is (/I)?
= BA cos or = BA
B = 0(N/l)I or I = Bl/(0N) L = N(/I) = N/I = NBA0N/Bl = 0N2A/l
L = 0n2Al
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Inductors
In a circuit any element with a high inductance is represented by an inductor
We will assume that the rest of the circuit has negligible inductance
Symbol is a spiral:
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Today’s PAL
A solenoid that is 5 cm long and 1 cm in diameter is placed in a circuit. If 0.1 V of emf is induced by increasing the current from 0 to 3 A in 0.5 seconds, how many turns does the solenoid have?
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RL Circuits
As current tries to flow, it is resisted by the inductor
Time depends on R and L
Current can’t get to max value or 0 instantly
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A RL Circuit
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Time Constant
The characteristic time is given as:
Larger inductance means longer delay
I = (/R)[1 - e(-t/)]
Note the similarities to a RC circuit
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Current Rise with Time
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Energy in an Inductor
This work can be thought of as energy stored in the inductor
E = (1/2) L I2
E and I are the values for the circuit after a “long time”
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Magnetic Energy
Where is this energy stored?
Magnetic fields, like electric fields both represent energy
B = (B2/20) This is how much energy per cubic meter is
stored in a magnetic field B
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Transforming Voltage
It is important to provide an electrical device with the right voltage
We often only have a single source of emf
We can use the fact that a voltage
through a solenoid will induce a magnetic field, which can induce an emf in another solenoid
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Basic Transformer
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Transformer
The emf then only depends on the number of turns in each
The ratio of emf’s is then just equal to the ratio of turns
Vp/Vs = Np/Ns
Device is called a transformer If Np > Ns, voltage decreases If Ns > Np voltage increases
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Transformers and Current
Energy is conserved in a transformer so: Vp/Vs = Is/Ip
Note that the flux must be
changing, and thus the current must be changing
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Transformer Applications
Generators usually operate at ~10,000 volts
Since P = I2R a small current is best for
transmission wires Power pole transformers step the voltage
down for household use to 120 or 240 V
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Next Time
Read 21.12 Homework, Ch 21, P 36, 43, 47, 53