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RL Circuits
Physics 102
Professor Lee Carkner
Lecture 21
PAL #21 Generator
To produce 12 amps in a 15 ohm wire
you need an emf of e = IR = (12)(15) =
180 V
Set 180 V equal to the max emf
e = NBAw
w = e/NBA = 180/(1)(2)(1) = 90 rad/s
If w = 90 rad/s, we can find f = w/2p
f = 14.3 Hz or 14.3 cycles per second
Induction and Circuits

The changing magnetic field can then induce
its own current that will oppose the initial
changes
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
 The emf induced opposes the direction of the current
change

 Called the back emf

 Current decreases, emf in same direction
Finding emf
The back emf depends on Faraday’s Law:
e = -N(DF/Dt)

If we put the coil properties into the variable “L”
we get:
e = -L(DI/Dt)

where the constant of proportionality L is the
inductance
The unit of inductance is the Henry,
H (V s/A)
Inductance

e = L(DI/Dt) = N(DF/Dt)
L = N(DF/DI)

L = m0n2Al
n=
A = cross sectional area
l = length
Inductors
In a circuit any element with a high
inductance is represented by an
inductor
Examples:
We will assume that the rest of the
circuit has negligible inductance

Symbol is a spiral:
Magnetic Energy
 A battery must do work to overcome the back emf of
a circuit with inductance

 Magnetic fields, like electric fields represent energy
 Energy in an inductor is:
E = (1/2) L I2

mB = (B2/2m0)
 This is how much energy per cubic meter is stored in a
magnetic field B
Transforming Voltage

We often only have a single source of emf
e.g. household current at 120 V

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
e = N(DF/Dt)

Vp/Vs = Np/Ns
Where p and s are the primary and secondary
solenoids

If Np > Ns, voltage decreases (is stepped down)
If Ns > Np voltage increases (is stepped up)
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
Transformers only work for AC current
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
A metal rod moves horizontally in a
uniform vertical magnetic field.
Which of the following changes would
not increase the emf induced across
the rod?
A) Increasing the strength of the
magnetic field
B) Increasing the velocity of the rod
C) Increasing the length of the rod
D) Increasing the thickness of the rod
E) Nothing can change the emf of the rod
Household electrical current has a
frequency of 60 Hz. What is its
angular frequency?
A)
B)
C)
D)
E)
9.5 rad/s
60 rad/s
188 rad/s
377 rad/s
600 rad/s
If the frequency of a generator is increased,
A) The maximum emf goes up and the current
changes direction more rapidly
B) The maximum emf goes up and the current
changes direction less rapidly
C) The maximum emf goes down and the
current changes direction more rapidly
D) The maximum emf goes down and the
current changes direction less rapidly
E) The maximum emf does not change