Module
5 AC Theory
Phasors
Phase and Phasor Diagrams
Introduction
What you'll learn in Module 5. The AC circuits described in this module are
some of the simplest in construction, consisting
5.1 Phase Shift of only two or three components, but in their
operation can seem almost magical, and are
Phase Shift in Common AC Components. amazingly useful in so many ways. They might
form the tuning circuit of a radio, and be used to
improve the performance of amplifiers. They
5.2 Phasors
can greatly magnify alternating voltages or
currents, and also reject radio interference. They
Use of Phasors to Simplify Complex Waveform may also be called "Tuned" or "Resonant"
diagrams. circuits and produce oscillations of a particular
pitch or frequency in musical instruments. They
Relationship Between Waveform and Phasor are used to separate the high, low and mid
Diagrams. range notes in a hi-fi speaker system. These
same circuits perform functions like sensing a
5.3 Phasor Diagrams car as it approaches a traffic light, or help find
buried precious metals with a metal detector.
Using Phasor Diagrams to Show Phase Difference.
As you study this and the following modules,
Drawing Phasor Diagrams. notice that the circuits described use two main
components, inductors and capacitors, which in
many ways seem to have opposite and
5.4 Phasor Calculations complimentary effects. It is the way they are
connected in a circuit, as well as their individual
Using Phasor Diagrams to Calculate Unknown electrical values that are key to the many uses
Values. of these circuits. Although in many cases these
basic inductor/capacitor combinations may now
Scale Drawings be replaced by new and usually smaller ceramic
components, the basic principles of these
Pythagoras´ Theorem LCR (inductor/capacitor/resistor) circuits are
essential to understanding the operation of
Trigonometry many electronic systems.
5.5 Phasor Quiz
Phasor Quiz
AC THEORY MODULE 05.PDF 1 E. COATES 2007 -2010
, www.learnabout-electronics.org Phase and Phasors
Module 5.1 Phase Shift
Fig 5.1.1 AC Phase Relationships in R, L and C
Resistance in AC Circuits
In purely resistive circuits, the current and voltage
both change in the same way, and at the same
time, as described in Module 4.1. This relationship
is true, whether the applied voltage is direct or
alternating. The main difference in AC circuits is
that the voltage continues to change in a way that
depends on the shape of the input wave. When a
sine wave voltage is applied to a purely resistive
circuit, it produces a sine wave (sinusoidal) current.
Both waveforms attain their peak values at the
same time, and pass through zero at the same
time. Voltage and current in a purely resistive circuit
are therefore said to be "IN PHASE" with each
other.
Inductance in AC Circuits
In a purely inductive circuit the voltage and
current waveforms are not in phase. Inductance
opposes change in current due to the back emf
effect. This causes the current to reach its peak
value some time after the voltage. So in an
inductive circuit, current "LAGS" voltage.
In DC circuits the current eventually settles to a
steady state value, and the period of change
prior to steady state depends on the time
constant (i.e. the component values) of the
circuit. In an AC circuit however, as the voltage is
continually changing, the current also continues to change, and in a purely inductive circuit, the peak
values of current occur a quarter of a cycle (90°) after those of the voltage.
In a circuit containing both inductance and resistance, which is usually the case as the inductor (a coil
of wire) will have some internal resistance, the current will lag the voltage by an amount between
practically 0° (nearly pure resistance) and almost −90° (nearly pure inductance). Since voltage and
current no longer rise and fall together, a "PHASE SHIFT" is occurring in the circuit.
Capacitance in AC Circuits
Capacitance has the property of delaying
changes in voltage as described in Module 4.3.
That is, the applied voltage reaches steady state
only after a time dictated by the time constant. In
AC circuits voltage and current are changing
continuously, and in a purely capacitive AC circuit
the peak value of the voltage waveform occurs a
quarter of a cycle after the peak value of the
current. Therefore a phase shift is occurring in
the capacitor, the amount of phase shift between
voltage and current is +90° for a purely capacitive
circuit, with the current LEADING the voltage.
The opposite phase shift to an inductive circuit.
AC THEORY MODULE 05.PDF 2 E. COATES 2007 -2017
5 AC Theory
Phasors
Phase and Phasor Diagrams
Introduction
What you'll learn in Module 5. The AC circuits described in this module are
some of the simplest in construction, consisting
5.1 Phase Shift of only two or three components, but in their
operation can seem almost magical, and are
Phase Shift in Common AC Components. amazingly useful in so many ways. They might
form the tuning circuit of a radio, and be used to
improve the performance of amplifiers. They
5.2 Phasors
can greatly magnify alternating voltages or
currents, and also reject radio interference. They
Use of Phasors to Simplify Complex Waveform may also be called "Tuned" or "Resonant"
diagrams. circuits and produce oscillations of a particular
pitch or frequency in musical instruments. They
Relationship Between Waveform and Phasor are used to separate the high, low and mid
Diagrams. range notes in a hi-fi speaker system. These
same circuits perform functions like sensing a
5.3 Phasor Diagrams car as it approaches a traffic light, or help find
buried precious metals with a metal detector.
Using Phasor Diagrams to Show Phase Difference.
As you study this and the following modules,
Drawing Phasor Diagrams. notice that the circuits described use two main
components, inductors and capacitors, which in
many ways seem to have opposite and
5.4 Phasor Calculations complimentary effects. It is the way they are
connected in a circuit, as well as their individual
Using Phasor Diagrams to Calculate Unknown electrical values that are key to the many uses
Values. of these circuits. Although in many cases these
basic inductor/capacitor combinations may now
Scale Drawings be replaced by new and usually smaller ceramic
components, the basic principles of these
Pythagoras´ Theorem LCR (inductor/capacitor/resistor) circuits are
essential to understanding the operation of
Trigonometry many electronic systems.
5.5 Phasor Quiz
Phasor Quiz
AC THEORY MODULE 05.PDF 1 E. COATES 2007 -2010
, www.learnabout-electronics.org Phase and Phasors
Module 5.1 Phase Shift
Fig 5.1.1 AC Phase Relationships in R, L and C
Resistance in AC Circuits
In purely resistive circuits, the current and voltage
both change in the same way, and at the same
time, as described in Module 4.1. This relationship
is true, whether the applied voltage is direct or
alternating. The main difference in AC circuits is
that the voltage continues to change in a way that
depends on the shape of the input wave. When a
sine wave voltage is applied to a purely resistive
circuit, it produces a sine wave (sinusoidal) current.
Both waveforms attain their peak values at the
same time, and pass through zero at the same
time. Voltage and current in a purely resistive circuit
are therefore said to be "IN PHASE" with each
other.
Inductance in AC Circuits
In a purely inductive circuit the voltage and
current waveforms are not in phase. Inductance
opposes change in current due to the back emf
effect. This causes the current to reach its peak
value some time after the voltage. So in an
inductive circuit, current "LAGS" voltage.
In DC circuits the current eventually settles to a
steady state value, and the period of change
prior to steady state depends on the time
constant (i.e. the component values) of the
circuit. In an AC circuit however, as the voltage is
continually changing, the current also continues to change, and in a purely inductive circuit, the peak
values of current occur a quarter of a cycle (90°) after those of the voltage.
In a circuit containing both inductance and resistance, which is usually the case as the inductor (a coil
of wire) will have some internal resistance, the current will lag the voltage by an amount between
practically 0° (nearly pure resistance) and almost −90° (nearly pure inductance). Since voltage and
current no longer rise and fall together, a "PHASE SHIFT" is occurring in the circuit.
Capacitance in AC Circuits
Capacitance has the property of delaying
changes in voltage as described in Module 4.3.
That is, the applied voltage reaches steady state
only after a time dictated by the time constant. In
AC circuits voltage and current are changing
continuously, and in a purely capacitive AC circuit
the peak value of the voltage waveform occurs a
quarter of a cycle after the peak value of the
current. Therefore a phase shift is occurring in
the capacitor, the amount of phase shift between
voltage and current is +90° for a purely capacitive
circuit, with the current LEADING the voltage.
The opposite phase shift to an inductive circuit.
AC THEORY MODULE 05.PDF 2 E. COATES 2007 -2017
