Lecture 10/5 Chapter 23/24 Flashcards
Self-inductance
o The inductance of a coil depends on
geometric factors
o The SI unit of self-inductance is the
Henry
o 1 H = 1 (V · s) / A
Self-inductance
You can determine an expression for L
L = N(∆ΦB/∆I) = (NΦB/I)
Quick Quiz
A solenoid used in magnetic
resonance imaging (MRI) is 2.4 m
long and 94 cm in diameter, with
1200 turns of superconducting wire.
Find the magnitude of the induced
emf in the solenoid during the 30 s
it takes to “ramp up” the current
from zero to its operating value of
2.3 kA. (µo = 4 π x 10-7 T.m / A)
a. 0.53 V
b. 10.0 V
c. 30.2 V
d. 40.1 V
a. 0.53 V
Inductor in a Circuit
o Inductance can be interpreted
as a measure of opposition to
the rate of change in the current
o Remember resistance R is a
measure of opposition to the
current
o As a circuit is completed, the
current begins to increase, but
the inductor produces an emf
that opposes the increasing
current
o Therefore, the current
doesn’t change from 0 to its
maximum instantaneously
Change of current happens faster than the rate of induction
RL Circuit
o When the current reaches its maximum,
the rate of change and the back emf are
zero
o The time constant, τ, for an RL circuit is
the time required for the current in the
circuit to reach 63.2% of its final value
The time constant depends on R and L
Equation
τ = L/R
The current at any time can be found by
I = (ε /R)(1 - e^(-t/τ)
Energy Stored in Inductors
o The emf induced by an inductor prevents
a battery from establishing an
instantaneous current in a circuit
o The battery has to do work to produce a
current
o This work can be thought of as energy stored
by the inductor in its magnetic field
Energy Stored in Inductors
Equation
UL = ½ L I^2
23-1 Induced Electromotive Force
* Faraday’s experiment:
closing the switch in the primary circuit induces a current in the secondary circuit, but only while the current in the primary circuit is changing.
23-2 Magnetic Flux
Magnetic flux is used in
the calculation of the
induced emf
23-3 Faraday’s Law of Induction:
An emf is induced only when the
magnetic flux through a loop changes with time
- There are many devices that operate on the
basis of Faraday’s law. - An electric guitar pickup
23-4 Lenz’s Law:
– An induced current always flows in a direction
that opposes the change that caused it.
– Therefore, if the magnetic field is increasing,
the magnetic field created by the induced
current will be in the opposite direction;
if decreasing,
it will be in the
same direction.
- This conducting rod completes the circuit. As it
falls, the magnetic flux decreases, and a current
is induced. - The force due to the induced current is upward, slowing the fall.
- Currents can also flow in bulk conductors. These induced currents, called eddy currents, can be powerful brakes.
AC Circuit
o An AC circuit consists of a
combination of circuit
elements and an AC generator
or source
o The output of an AC generator
is sinusoidal and varies with
time according to the following
equation
o Δv = ΔVmax sin 2πƒt
o Δv is the instantaneous
voltage
o ΔVmax is the maximum
voltage of the
generator
o ƒ is the frequency at
which the voltage
changes, in Hz
Resistor in an AC Circuit
o The current and the voltage reach
their maximum values at the same
time
o The current and the voltage are said
to be in phase
o The direction of the current has no effect on the behavior of the resistor
o The rate at which electrical energy is dissipated in the circuit is given by
℘ = = i^(2) R
o where i is the instantaneous current
o the heating effect produced by an AC current with a maximum
value of Imax is not the same as that of a DC current of the same
value
o The maximum current occurs for a small amount of time
rms Current and Voltage
- The voltage and current in an ac circuit both average to zero,
making the average useless in describing their behavior. - We use instead the root mean square (rms); we square the value,
find the mean value, and then take the square root. - 120 volts is the rms value of household ac.
The rms current is the direct current that would dissipate the same
amount of energy in a resistor as is actually dissipated by the AC current
- equation
Alternating voltages can also be discussed in terms of rms values
- equation
Ohm’s Law for a resistor, R, in an AC circuit
o ΔVR,rms = Irms R
o Also applies to the maximum values of v
and i
The average power dissipated in resistor in an
AC circuit carrying a current I is
℘ av = I^2 (rms) R
Quick Quiz
The rms current is equal to the direct current that:
a. produces the same average voltage across a resistor as in an AC circuit.
b. dissipates an equal amount of energy in a resistor at the same rate as in an AC circuit.
c. provides the same average current in a resistor as in an AC circuit.
d. results in the same peak power in a resistor as in an AC circuit.
Capacitors in an AC Circuit
o The impeding effect of a capacitor
on the current in an AC circuit is
called the capacitive reactance
and is given by
Xc = (1/2πfC)
o When ƒ is in Hz and C is in F,
Xc will be in ohms
o Ohm’s Law for a capacitor in an
AC circuit
o ΔVC,rms = Irms Xc
Inductors in an AC Circuit
o The effective resistance of a coil in an AC circuit is called its inductive reactance and is given by
o XL = 2πƒL =ωL
o When ƒ is in Hz and L is in H, XL will be in ohms
o Ohm’s Law for the inductor
o ΔVL,rms = Irms XL
Quick Quiz
The frequency in an AC series circuit is
doubled. By what factor does this change the
capacitive reactance?
a. 1/2
b. 1/4
c. 2
d. 4
The RLC Series Circuit
The current in the circuit is the
same at any time and varies
sinusoidally with time
ΔV, net instantaneous voltage
