Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
Class 13
Impedance in AC Crcuits
Physics 106
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Press CTRL-L to view as a slide show.
Learning Outcomes
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Last time we
Resistors,
Capacitors, and
Inductors in AC
Circuits
I
learned about generators
I
looked at the details of a motional emf problem
The Series RLC
Circuit
I
reviewed for Exam #1
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Learning Outcomes
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Last time we
Resistors,
Capacitors, and
Inductors in AC
Circuits
I
learned about generators
I
looked at the details of a motional emf problem
The Series RLC
Circuit
I
reviewed for Exam #1
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Learning Outcomes
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Last time we
Resistors,
Capacitors, and
Inductors in AC
Circuits
I
learned about generators
I
looked at the details of a motional emf problem
The Series RLC
Circuit
I
reviewed for Exam #1
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Learning Outcomes
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
Today we will discuss:
I
Inductors and self-inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Learning Outcomes
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
Today we will discuss:
I
Inductors and self-inductance
I
RL Circuit Problems
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Learning Outcomes
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
Today we will discuss:
I
Inductors and self-inductance
I
RL Circuit Problems
I
AC Circuit Terminology
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Learning Outcomes
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
Today we will discuss:
I
Inductors and self-inductance
I
RL Circuit Problems
I
AC Circuit Terminology
I
R, L, and C in AC Circuits
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Inductors and
Self-Inductance
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Self-inductance
Class 13
Physics 106
Learning
Outcomes
I
A coil of wire in a circuit is called an inductor. It
produces a magnetic field inside itself.
I
If the current is changing, it produces an EMF
because its own B field is changing in time.
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Self-inductance
Class 13
Physics 106
Learning
Outcomes
I
A coil of wire in a circuit is called an inductor. It
produces a magnetic field inside itself.
I
If the current is changing, it produces an EMF
because its own B field is changing in time.
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Self-inductance
Class 13
Physics 106
Learning
Outcomes
I
If current is increasing, the inductor produces an
induced current that opposes the current in the
circuit.
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Self-inductance
Class 13
Physics 106
Learning
Outcomes
I
If current is decreasing, the inductor produces an
induced current in the direction of the current in the
circuit.
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Self-inductance
Class 13
Physics 106
Learning
Outcomes
I
The faster the current changes, the larger the is the
induced EMF
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Class 13
Self-inductance
Physics 106
Learning
Outcomes
I
We define the inductance L of a coil by the
relationship:
= −L
∆I
∆t
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Class 13
Self-inductance
Physics 106
Learning
Outcomes
I
We define the inductance L of a coil by the
relationship:
= −L
I
∆I
∆t
The negative sign indicates that a changing current
induces an emf in opposition to that change
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Self-inductance
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
The SI unit of self-inductance is the Henry (H)
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Class 13
Self-inductance
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
The SI unit of self-inductance is the Henry (H)
AC Circuit
Terminology
I
A useful expression for L is:
Resistors,
Capacitors, and
Inductors in AC
Circuits
ΦB
L=N
I
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
RL Circuits
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Inductors in a Circuit
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
If an inductor, a resistor, a battery, and a switch are
placed in in a series circuit:
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Inductors in a Circuit
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
If an inductor, a resistor, a battery, and a switch are
placed in in a series circuit:
I Just after the switch is closed, the inductor
produces an emf that completely stops the flow
of current− but only instantaneously
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Inductors in a Circuit
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
If an inductor, a resistor, a battery, and a switch are
placed in in a series circuit:
I Just after the switch is closed, the inductor
produces an emf that completely stops the flow
of current− but only instantaneously
I After a long time, the inductor acts like a wire.
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
RL Circuit
Class 13
Physics 106
I
As the current
gets larger, it
changes less, and
the inductor’s
voltage
decreases.
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
RL Circuit
Class 13
Physics 106
I
I
As the current
gets larger, it
changes less, and
the inductor’s
voltage
decreases.
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
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Class 13
RL Circuit
Physics 106
Learning
Outcomes
I
The time constant depends on R and L
τ=
L
R
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Class 13
RL Circuit
Physics 106
Learning
Outcomes
I
The time constant depends on R and L
τ=
L
R
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
I
The current at any time can be found by
−t/τ
I=
1−e
R
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Energy Stored in a Magnetic Field
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
I
An inductor stores energy in its magnetic field.
1
UL = LI 2
2
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
RL Circuit Example
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
I
A 3.0 Ω resistor, a 12 mH inductor, and a 12 V battery
are connected in series. A switch is closed at t = 0.
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
AC Circuit Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
AC Circuit
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
The output of an AC generator is sinusoidal and
varies with time according to the following equation
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
AC Circuit
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
The output of an AC generator is sinusoidal and
varies with time according to the following equation
I
V (t) = Vmax sin 2πft
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
AC Circuit
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
The output of an AC generator is sinusoidal and
varies with time according to the following equation
I
V (t) = Vmax sin 2πft
I
V (t) is the instantaneous voltage
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
AC Circuit
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
The output of an AC generator is sinusoidal and
varies with time according to the following equation
I
V (t) = Vmax sin 2πft
I
I
V (t) is the instantaneous voltage
Vmax is the maximum voltage of the generator
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
AC Circuit
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
The output of an AC generator is sinusoidal and
varies with time according to the following equation
I
V (t) = Vmax sin 2πft
I
I
I
V (t) is the instantaneous voltage
Vmax is the maximum voltage of the generator
f is the frequency at which the voltage changes,
in Hz
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
AC Circuit
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
The output of an AC generator is sinusoidal and
varies with time according to the following equation
I
V (t) = Vmax sin 2πft
I
I
I
I
V (t) is the instantaneous voltage
Vmax is the maximum voltage of the generator
f is the frequency at which the voltage changes,
in Hz
The period is T = 1/f
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Average Voltage
Class 13
Physics 106
I
V (t) = Vmax sin 2πft
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Average Voltage
Class 13
Physics 106
I
V (t) = Vmax sin 2πft
I
The average value of sine is 0
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Average Voltage
Class 13
Physics 106
I
V (t) = Vmax sin 2πft
I
The average value of sine is 0
I
But that’s not useful
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Average Voltage
Class 13
Physics 106
Learning
Outcomes
I
We could try Vmax | sin 2πft |
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Average Voltage
Class 13
Physics 106
Learning
Outcomes
I
We could try Vmax | sin 2πft |
Inductors and
Self-Inductance
I
But absolute values are awkward functions.
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Average Voltage
Class 13
Physics 106
Learning
Outcomes
I
2
Try Vmax
sin2 2πft
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Average Voltage
Class 13
Physics 106
Learning
Outcomes
I
2
Try Vmax
sin2 2πft
I
The average value of sin2 is 1/2
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Average Voltage
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
2
Try Vmax
sin2 2πft
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Class 13
Average Voltage
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
I
2
Try Vmax
sin2 2πft
2
But this is the average value of sin
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Class 13
Average Voltage
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
2
Try Vmax
sin2 2πft
2
I
But this is the average value of sin
I
So we take the square root of this
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Class 13
Average Voltage
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
2
Try Vmax
sin2 2πft
2
I
But this is the average value of sin
I
So we take the square root of this
I
This is called the root-mean-square or "rms" voltage.
Vrms
Vmax
= √
2
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
rms Values
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
rms values are the most practical effective values for
AC circuits
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
rms Values
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
rms values are the most practical effective values for
AC circuits
I
We can have rms voltages or currents
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
rms Values
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
rms values are the most practical effective values for
AC circuits
I
We can have rms voltages or currents
I
Our outlets have 110-120 V rms.
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Class 13
rms Values
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
rms values are the most practical effective values for
AC circuits
I
We can have rms voltages or currents
I
Our outlets have 110-120 V rms.
Vrms
Vmax
= √
2
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
AC Circuit
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
rms values will be used when discussing AC currents
and voltages
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
AC Circuit
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
rms values will be used when discussing AC currents
and voltages
I AC ammeters and voltmeters are designed to
read rms values
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
AC Circuit
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
rms values will be used when discussing AC currents
and voltages
I AC ammeters and voltmeters are designed to
read rms values
I Many of the equations will be in the same form
as in DC circuits
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors, Capacitors, and
Inductors in AC Circuits
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Resistor in an AC Circuit
Class 13
Physics 106
I
Consider a circuit
consisting of an AC
source and a resistor
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Resistor in an AC Circuit
Class 13
Physics 106
I
I
Consider a circuit
consisting of an AC
source and a resistor
The graph shows the
current through and
the voltage across
the resistor
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Resistor in an AC Circuit
Class 13
Physics 106
I
I
I
Consider a circuit
consisting of an AC
source and a resistor
The graph shows the
current through and
the voltage across
the resistor
The current and the
voltage reach their
maximum values at
the same time
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Resistor in an AC Circuit
Class 13
Physics 106
I
I
I
I
Consider a circuit
consisting of an AC
source and a resistor
The graph shows the
current through and
the voltage across
the resistor
The current and the
voltage reach their
maximum values at
the same time
The current and the
voltage are said to
be in phase
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Ohm’s Law in an AC Circuit
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
Ohm’s Law for a resistor, R, in an AC circuit
VR,rms = Irms R
or
VR,max = Imax R
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Capacitors and Inductors in AC Circuits
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
Ohm’s Law for a capacitor or inductor in an AC
circuit:
VC,rms = Irms XC
VL,rms = Irms XL
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Capacitors and Inductors in AC Circuits
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
Ohm’s Law for a capacitor or inductor in an AC
circuit:
VC,rms = Irms XC
VL,rms = Irms XL
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
I
The effective resistance is called "reactance"
Phasors in the
Series RLC
Circuit
Impedance
Power
Capacitors and Inductors in AC Circuits
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
Ohm’s Law for a capacitor or inductor in an AC
circuit:
VC,rms = Irms XC
VL,rms = Irms XL
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
I
The effective resistance is called "reactance"
I
Remember ELI the ICE man
Phasors in the
Series RLC
Circuit
Impedance
Power
Capacitors in an AC Circuit
Class 13
Physics 106
Learning
Outcomes
I
The voltage
across the
capacitor lags
behind the
current by 90◦
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Capacitors in an AC Circuit
Class 13
Physics 106
Learning
Outcomes
I
I
The voltage
across the
capacitor lags
behind the
current by 90◦
I in a capacitor,
C, reaches its
maximum
before the EMF
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Capacitors in an AC Circuit
Class 13
Physics 106
Learning
Outcomes
I
I
The voltage
across the
capacitor lags
behind the
current by 90◦
I in a capacitor,
C, reaches its
maximum
before the EMF
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Capacitors in an AC Circuit
Class 13
Physics 106
Learning
Outcomes
I
I
I
The voltage
across the
capacitor lags
behind the
current by 90◦
I in a capacitor,
C, reaches its
maximum
before the EMF
Positive voltage
opposes
current flow, as
a resistor.
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Capacitive Reactance and Ohm’s Law
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
The effective resistance in a capacitor is called
capacitive reactance,
XC =
1
2πfC
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
I
The SI unit of XC is ohms
I
Ohm’s law for a capacitor in an AC circuit is
VC,rms = Irms XC
Phasors in the
Series RLC
Circuit
Impedance
Power
Capacitive Reactance and Ohm’s Law
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
The effective resistance in a capacitor is called
capacitive reactance,
XC =
1
2πfC
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
I
The SI unit of XC is ohms
I
Ohm’s law for a capacitor in an AC circuit is
VC,rms = Irms XC
Phasors in the
Series RLC
Circuit
Impedance
Power
Capacitive Reactance and Ohm’s Law
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
The effective resistance in a capacitor is called
capacitive reactance,
XC =
1
2πfC
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
I
The SI unit of XC is ohms
I
Ohm’s law for a capacitor in an AC circuit is
VC,rms = Irms XC
Phasors in the
Series RLC
Circuit
Impedance
Power
Capacitive Reactance and Ohm’s Law
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
A capacitor has a large effective resistance when it
builds up a large voltage to oppose current flow.
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
1
XC =
2πfC
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Capacitive Reactance and Ohm’s Law
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
A capacitor has a large effective resistance when it
builds up a large voltage to oppose current flow.
I
Large capacitances have small voltages, V = Q/C.
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
1
XC =
2πfC
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Capacitive Reactance and Ohm’s Law
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
I
A capacitor has a large effective resistance when it
builds up a large voltage to oppose current flow.
I
Large capacitances have small voltages, V = Q/C.
Resistors,
Capacitors, and
Inductors in AC
Circuits
I
If the frequency is large, the capacitor doesn’t have a
chance to build up large voltages.
The Series RLC
Circuit
1
XC =
2πfC
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Inductors in an AC Circuit
Class 13
Physics 106
I
The current is
affected by the
emf of the
inductor
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Inductors in an AC Circuit
Class 13
Physics 106
I
I
The current is
affected by the
emf of the
inductor
The voltage
across the
inductor always
leads the
current by 90◦
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Inductors in an AC Circuit
Class 13
Physics 106
I
I
I
The current is
affected by the
emf of the
inductor
The voltage
across the
inductor always
leads the
current by 90◦
EMF in an
inductor, L,
reaches its
maximum
before I
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Inductors in an AC Circuit
Class 13
Physics 106
I
I
I
The current is
affected by the
emf of the
inductor
The voltage
across the
inductor always
leads the
current by 90◦
EMF in an
inductor, L,
reaches its
maximum
before I
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Inductive Reactance and Ohm’s Law
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
The effective resistance in an inductor is called
AC Circuit
Terminology
inductive reactance,
Resistors,
Capacitors, and
Inductors in AC
Circuits
XL = 2πfL
I
The SI unit of XC is ohms
I
Ohm’s law for an inductor in an AC circuit is
VL,rms = Irms XL
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Inductive Reactance and Ohm’s Law
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
The effective resistance in an inductor is called
AC Circuit
Terminology
inductive reactance,
Resistors,
Capacitors, and
Inductors in AC
Circuits
XL = 2πfL
I
The SI unit of XC is ohms
I
Ohm’s law for an inductor in an AC circuit is
VL,rms = Irms XL
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Inductive Reactance and Ohm’s Law
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
The effective resistance in an inductor is called
AC Circuit
Terminology
inductive reactance,
Resistors,
Capacitors, and
Inductors in AC
Circuits
XL = 2πfL
I
The SI unit of XC is ohms
I
Ohm’s law for an inductor in an AC circuit is
VL,rms = Irms XL
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Inductive Reactance and Ohm’s Law
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
An inductor has a large effective resistance when it
has a large emf.
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
XL = 2πfL
Phasors in the
Series RLC
Circuit
Impedance
Power
Inductive Reactance and Ohm’s Law
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
I
An inductor has a large effective resistance when it
has a large emf.
Large inductances have large emf’s.
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
XL = 2πfL
Phasors in the
Series RLC
Circuit
Impedance
Power
Inductive Reactance and Ohm’s Law
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
An inductor has a large effective resistance when it
has a large emf.
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
I
Large inductances have large emf’s.
I
If the frequency is large, the inductor produces a
large emf
The Series RLC
Circuit
XL = 2πfL
Phasors in the
Series RLC
Circuit
Phasors
Impedance
Power
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
The Series RLC Circuit
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
The RLC Series Circuit
Class 13
Physics 106
Learning
Outcomes
I
A resistor,
inductor, and
capacitor can be
combined with an
AC power supply
in a series circuit
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
The RLC Series Circuit
Class 13
Physics 106
Learning
Outcomes
I
I
A resistor,
inductor, and
capacitor can be
combined with an
AC power supply
in a series circuit
The current in the
circuit is the same
at any time and
varies sinusoidally
with time
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Current and Voltage Relationships in an
RLC Circuit
Class 13
Physics 106
Learning
Outcomes
I
The instantaneous
voltage across the
resistor is in phase
with the current
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Current and Voltage Relationships in an
RLC Circuit
Class 13
Physics 106
Learning
Outcomes
I
I
The instantaneous
voltage across the
resistor is in phase
with the current
The instantaneous
voltage across the
inductor leads the
current by 90◦
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Current and Voltage Relationships in an
RLC Circuit
Class 13
Physics 106
Learning
Outcomes
I
I
I
The instantaneous
voltage across the
resistor is in phase
with the current
The instantaneous
voltage across the
inductor leads the
current by 90◦
The instantaneous
voltage across the
capacitor lags the
current by 90◦
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Current and Voltage Relationships in an
RLC Circuit
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
I
The voltages across
the R, L, and C add
to equal the voltage
of the power supply
at all times
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Current and Voltage Relationships in an
RLC Circuit
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
I
I
The voltages across
the R, L, and C add
to equal the voltage
of the power supply
at all times
Currents are the
same everywhere
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Summary of Circuit Elements, Impedance
and Phase Angles
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Phasors and the Series
RLC Circuit
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Current and Voltage Relationships in an
RLC Circuit
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
When we add current
and voltages in AC
circuits, we have to
use the values at one
specific time.
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Current and Voltage Relationships in an
RLC Circuit
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
I
When we add current
and voltages in AC
circuits, we have to
use the values at one
specific time.
The hard way is to
write sine and cosine
functions and use
trig identities.
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Current and Voltage Relationships in an
RLC Circuit
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
I
I
When we add current
and voltages in AC
circuits, we have to
use the values at one
specific time.
The hard way is to
write sine and cosine
functions and use
trig identities.
The easy way is to
use "phasors."
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Representing an AC Current
Class 13
Physics 106
I
If a current varies sinusoidally, we usually represent it
graphically.
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Representing an AC Current
Class 13
Physics 106
I
But we can also represent it with an arrow that goes
up and down in time.
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Representing an AC Current
Class 13
Physics 106
I
I
An arrow that goes up and down sinusoidally is just
the y component of a vector that rotates at a
constant angular frequency.
The length of the arrow is i0 and the angle of the
vector is θ = 2πft.
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Representing an AC Current
Class 13
Physics 106
I
I
An arrow that goes up and down sinusoidally is just
the y component of a vector that rotates at a
constant angular frequency.
The length of the arrow is i0 and the angle of the
vector is θ = 2πft.
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Phasors
Class 13
Physics 106
I
A phasor is a vector that represents a sinusoidal
function. Its magnitude is the amplitude of the sine
wave (it’s maximum value) and its angle is the phase
angle (the argument of the sine function).
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Phasor Diagrams
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
We represent the
current or voltage
across each
element as a
phasor
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Phasor Diagrams
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
I
We represent the
current or voltage
across each
element as a
phasor
The diagram is
called a phasor
diagram
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Phasor Diagram for RLC Series Circuit
Class 13
Physics 106
Learning
Outcomes
I
Let I =
Imax sin(2πft).
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Phasor Diagram for RLC Series Circuit
Class 13
Physics 106
Learning
Outcomes
I
Let I =
Imax sin(2πft).
I
At time t = 0, the
current is 0.
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Phasor Diagram for RLC Series Circuit
Class 13
Physics 106
Learning
Outcomes
I
Let I =
Imax sin(2πft).
I
At time t = 0, the
current is 0.
I
Since the current
is the
y -component of
the phasor, at
time t = 0, the
current phasor is
in the x direction.
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Phasor Diagram for RLC Series Circuit
Class 13
Physics 106
I
The voltage across
the resistor is on the
+x axis since it is in
phase with the
current
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Phasor Diagram for RLC Series Circuit
Class 13
Physics 106
I
I
The voltage across
the resistor is on the
+x axis since it is in
phase with the
current
The voltage across
the inductor is on the
+y axis since it leads
the current by 90◦
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Phasor Diagram for RLC Series Circuit
Class 13
Physics 106
I
I
I
The voltage across
the resistor is on the
+x axis since it is in
phase with the
current
The voltage across
the inductor is on the
+y axis since it leads
the current by 90◦
The voltage across
the capacitor is on
the −y axis since it
lags behind the
current by 90◦
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Resistor Phasors in Time
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Inductor Phasors in Time
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Capacitor Phasors in Time
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Phasors in the Series
RLC Circuit
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Circuit Rules for AC Circuits
Class 13
Physics 106
Learning
Outcomes
If two circuit elements are in series:
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Circuit Rules for AC Circuits
Class 13
Physics 106
Learning
Outcomes
If two circuit elements are in series:
1)their current phasors are the same.
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Circuit Rules for AC Circuits
Class 13
Physics 106
Learning
Outcomes
If two circuit elements are in series:
1) their current phasors are the same.
2) their voltage phasors add to give the total voltage.
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Phasor Diagram
Class 13
Physics 106
Learning
Outcomes
I
The phasors are
added as vectors to
account for the
phase differences in
the voltages
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Phasor Diagram
Class 13
Physics 106
Learning
Outcomes
I
I
The phasors are
added as vectors to
account for the
phase differences in
the voltages
VL and VC are in
opposite directions
line and so the net y
component is
VL − VC
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Phasor Diagram
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
I
VR is on the x axis,
so it is at right angles
to VL − VC
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Phasor Diagram
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
I
VR is on the x axis,
so it is at right angles
to VL − VC
I
Vmax is the vector
sum of VL − VC and
VR
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Impedance of a Circuit
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
Divide each
side of the
voltage triangle
by the current
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Impedance of a Circuit
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
Divide each
side of the
voltage triangle
by the current
VR
=R
I
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Impedance of a Circuit
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
Divide each
side of the
voltage triangle
by the current
VL − VC
= XL −XC
I
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Impedance of a Circuit
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
Divide each
side of the
voltage triangle
by the current
Vmax
=Z
I
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Impedance of a Circuit
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
The angle
between the
power supply
voltage and the
current is
−1
φ = tan
XL − XC
R
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Impedance and Ohm’s Law
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
I
Ohm’s Law can be applied to the impedance
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Impedance and Ohm’s Law
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
I
Ohm’s Law can be applied to the impedance
I
Vmax = Imax Z
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Impedance and Ohm’s Law
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
I
Ohm’s Law can be applied to the impedance
I
Vmax = Imax Z
I
This can be regarded as a generalized form of Ohm’s
Law applied to a series AC circuit
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Summary of Circuit Elements, Impedance
and Phase Angles
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Power in an AC Circuit
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
No power losses are associated with pure capacitors
and pure inductors in an AC circuit
I
In a capacitor, during one-half of a cycle energy is
stored and during the other half the energy is
returned to the circuit
I
In an inductor, the source does work against the
back emf of the inductor and energy is stored in the
inductor, but when the current begins to decrease in
the circuit, the energy is returned to the circuit
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Power in an AC Circuit
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
No power losses are associated with pure capacitors
and pure inductors in an AC circuit
I
In a capacitor, during one-half of a cycle energy is
stored and during the other half the energy is
returned to the circuit
I
In an inductor, the source does work against the
back emf of the inductor and energy is stored in the
inductor, but when the current begins to decrease in
the circuit, the energy is returned to the circuit
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Power in an AC Circuit
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
I
No power losses are associated with pure capacitors
and pure inductors in an AC circuit
I
In a capacitor, during one-half of a cycle energy is
stored and during the other half the energy is
returned to the circuit
I
In an inductor, the source does work against the
back emf of the inductor and energy is stored in the
inductor, but when the current begins to decrease in
the circuit, the energy is returned to the circuit
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Power Dissipated by a Resistor
Class 13
Physics 106
Learning
Outcomes
Inductors and
Self-Inductance
AC Circuit
Terminology
I
The average power dissipated in resistor in an AC
circuit carrying a current I is
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
2
Pave = Irms
R
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Power in an AC Circuit
Class 13
Physics 106
Learning
Outcomes
I
The average power
delivered by the
generator is
converted to internal
energy in the resistor
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Power in an AC Circuit
Class 13
Physics 106
Learning
Outcomes
I
I
The average power
delivered by the
generator is
converted to internal
energy in the resistor
Pav = Irms VR =
Irms Vsource cos φ
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power
Power in an AC Circuit
Class 13
Physics 106
Learning
Outcomes
I
I
I
The average power
delivered by the
generator is
converted to internal
energy in the resistor
Pav = Irms VR =
Irms Vsource cos φ
cosφ is called the
power factor of the
circuit
Inductors and
Self-Inductance
AC Circuit
Terminology
Resistors,
Capacitors, and
Inductors in AC
Circuits
The Series RLC
Circuit
Phasors
Phasors in the
Series RLC
Circuit
Impedance
Power