rl circuits physics 102 professor lee carkner lecture 22
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RL Circuits
Physics 102Professor Lee
CarknerLecture 22
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 =
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
Self Inductance
When the switch is closed, current flows through the loop, inducing a B field through the loop
Called self inductance
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
Inductance and Increasing
Current
Effect of Back emf
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
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
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
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:
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?
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
A RL Circuit
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
Current Rise with Time
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”
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
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
Basic Transformer
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
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
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
Next Time
Read 21.12 Homework, Ch 21, P 36, 43, 47, 53