ELEC176 Electronics I
July 30, 2001
Electronics deals with the study of energy carried by the
electric charge of electrons and the controlling of that energy by electric circuits to do useful tasks.
electric adj. & n. adj.
1 of, worked by, or charged with electricity; producing or capable of generating electricity.
2 causing or charged with sudden and dramatic excitement (the news had an
electric effect; the atmosphere was electric).
n.
1 an electric light, vehicle, etc.
2 (in pl.) electrical equipment.
electrically adv.
[modern Latin electricus via Latin electrum from Greek ¯elektron ‘amber’, the rubbing of which causes electrostatic phenomena]
electricity n.
1 a form of energy resulting from the existence of charged particles (electrons, protons, etc.), either statically as an accumulation of charge or dynamically as a current.
2 the branch of physics dealing with electricity.
3 a supply of electric current for heating, lighting, etc.
4 a state of heightened emotion; excitement, tension.
electronics n.pl.
1 (treated as sing.) the branch of physics and technology concerned with the behaviour and movement of electrons in a vacuum, gas, semiconductor, etc.
2 (treated as pl.) the circuits used in this.
ELEC176 - Introduction ELEC176 - Introduction
•
An electric circuit or network is a collection of connected devices through which electric charge is conveyed.
•
The behaviour of a circuit is investigated with circuit
analysis.
•
Fundamental physical quantities used to describe the state of a circuit are:
– Energy and Charge - related by voltage
– Power and Current - rates of energy and charge
•
Energy
– Unit of work: joule [J]
Energy and work have the same units.
Energy, measured in joules, is required to do useful work.
•
Charge
– Unit of charge: coulomb [C]
Charge conveys energy for useful work.
The amount of charge is measured in coulombs.
i
ELEC176 - Introduction ii ELEC176 - Energy and Charge 1-1

Charge loses or gains energy as it moves from place to place.
Each coulomb goes from having one value of potential energy (joules) to having another.
The potential energy per unit charge is called the
Electric Potential of the charge.
Thus, the Electric Potential of charge changes from one position to another. This change is measured as a Potential
Difference.
•
Unit of Potential Difference: volt [V],
One volt [V] is a change of one joule per coulomb [J/C].
Q coulombs [C] of charge moving through a potential difference of v volts [V] experience a change in energy of w
=
Qv joules [J]:
ELEC176 - Energy and Charge 1-2
The fundamental units of potential difference, or voltage, relate as: [J]
=
[C][V]
•
If there is a higher potential difference, then
– the same amount of work can be done by less charge, or
– the same amount of charge can do more work.
Examples: antenna signal microphone signal (quiet source) audio “line” level (CD player) supply voltage for most circuits car battery residential power power distribution colour tv tube acceleration potential long-haul power transmission breakdown potential in air
(depends on humidity) safe potentials (if touched) dangerous potentials
1 µ V
1 µ V
100 mV
1.8 V to 12 V
12 V
240 V
10,000 V
10,000 V
200 kV
7 kV/cm
< 50 V
> 200 V
ELEC176 - Energy and Charge 1-3
A voltage source generates a potential difference.
The potential energy of charge is changed by passing it through a voltage source. The energy may be increased or decreased, depending on the direction of charge flow.
A battery is a reasonable voltage source that generates a potential difference between its two terminals. Charge can enter one terminal while the same amount leaves the other terminal. It appears that charge can pass through the battery and, as it does so, its potential energy is changed by the battery.
The work done by the potential difference depends upon
what is connected to the voltage source.
•
A 9V battery.
If charge enters the negative terminal and leaves the positive terminal, then the energy per coulomb is increased by 9 V.
The battery would impart 36 J of energy to +4 C of charge:
9
V
=
36
4
C
J
36 J can operate a transistor radio for about 40 hours.
•
Starting a car.
About 3000 J is required to start a car engine. The 12V battery in a car is used to do this.
The battery supplies 12 J to each coulomb that passes through, so
250
C
=
3000
12
V of charge must flow to start the car.
J
ELEC176 - Energy and Charge 1-4 ELEC176 - Energy and Charge 1-5

Node: a point in a circuit, or set of connected points that are at the same Electric Potential.
•
Between different nodes in a circuit there is a potential difference.
•
When moving charge between nodes:
– energy change can be positive or negative
A positive charge experiences a positive energy change if it moves to a node of higher Electric
Potential.
– the charge can be positive or negative
If the energy of positive charge increases when it is moved from Node A to Node B, then the energy of negative charge moved in the same direction would decrease.
Electrons have a charge of
− 1
.
609 × 10 − 19
C.
•
Thus to determine the sign of the Potential Difference between two nodes it is necessary to consider
– the sign of the charge,
– the direction the charge moves, and
– the sign of the change in energy.
ELEC176 - Energy and Charge 1-6
Since Potential Difference can be positive or negative, battery terminals are labelled
(+) and
( − )
.
•
Starting a car engine
About -250 C from the
( − ) terminal of the battery flows through the starter motor and back to the
(+) terminal.
The battery adds
− 12 × − 250
J of its stored chemical energy to the charge flowing from
(+) to
( − )
INSIDE it.
Positive charge flowing in the opposite direction can also start the car.
+12 × +250
J would be added to +250 C of charge flowing in the opposite direction,
( − ) to
(+)
, INSIDE the battery.
•
Charging the Battery
When the engine is running, the battery is recharged.
–250 C from the
(+) terminal of the battery flows through an alternator and back into the
( − ) terminal.
The alternator (a type of voltage source) adds energy to the charge.
The energy of the charge flowing from
( − ) to
(+)
INSIDE the battery is DECREASED as the battery restores its stored chemical energy.
Positive charge would flow in the opposite direction.
ELEC176 - Energy and Charge 1-7
Circuit symbols are used to represent circuits on paper.
+
12 V
Terminal
+
12 V
Connection
Value
Battery
Terminal
Features: terminals and connections via drawn lines.
The potential difference is established between the
terminals of the battery.
The circuit symbol indicates the polarity of the battery.
The value indicates the potential difference.
The
+ terminal is at a higher electric potential if the value is positive.
ELEC176 - Energy and Charge 1-8
An ideal voltage source establishes a potential difference that is a known function of time and is independent of current.
+ v
( t
)
The symbol includes a value ( v
( t
)
) and polarity (
+
).
The
+ terminal is at a higher electric potential if v
( t
)
>
0
.
ELEC176 - Energy and Charge 1-9

Batteries store finite energy and have a maximum rate of charge movement.
If the charge flow rate is changed, the potential difference is changed.
As the stored energy is transferred to charge, the potential difference reduces — the battery goes flat.
Before this, a battery can be modelled as an ideal voltage source generating a constant potential difference.
v
( t
)
+
V
V t
•
Whenever possible, a system will reduce its potential energy. A ball will drop, or charge moves, to a state of lower potential energy.
•
Consequently, since w
=
Q v :
– +ve charge is attracted to a lower electric potential.
– –ve charge is attracted to a higher electric potential.
As the charge moves, it does work to release its potential energy.
•
To move charge in the opposite direction requires work by something else. This happens inside a battery or voltage source.
The potential energy of charge can be increased by batteries and voltage sources.
•
Current is movement of charge, and when work is done, the energy of the charge is changed.
ELEC176 - Energy and Charge 1-10 ELEC176 - Power and Current 2-1
The rates of ‘energy change’ and ‘charge flow’ are
Power and Current.
•
Power
– Rate of doing work: watt [W]
One watt [W] is an energy change of one joule per second [J/s].
For a system with energy w
( t
)
, a function of time, the power entering is p
( t
) = d w
( t
) dt
•
Current
– Flow or rate of change in charge: ampere [A]
One ampere [A], abbreviated ‘amp,’ is charge flowing (or changing) at a rate of one coulomb per second [C/s].
For a region with charge q
( t
)
, a function of time, the current entering is i
( t
) = d q
( t
) dt
ELEC176 - Power and Current 2-2 ELEC176 - Power and Current
•
Example: Work of carrying a person up the lecture theatre to look at the wall.
Run up and much force is required to do this.
Walk up and the same work is done to carry a person, but less force is required to do this.
The difference is the power, or rate of doing the work.
•
Power is a better measure of the force required to perform a task.
– Doing 3000 J of work in 1000 seconds requires (on average) only 3 watts of power. (A D-size battery could do this.)
– Doing 3000 J of work in 4 seconds, starting a car, requires (on average) 750 watts of power.
2-3

•
Charge moving at a rate i [A] loses or gains energy at a rate p [W] as it moves from place to place. It goes from having one value of potential energy to having another as it moves from place to place.
That is, the Electric Potential of the charge also changes from one position to another.
A potential difference of one volt [V=J/C] gives a rate of energy change of one watt [W=J/s] per ampere [A=C/s].
v
( t
) = p
( t
) i
( t
)
= dw ( t ) dt dq
( t
) dt
= dw dq
•
Instantaneous Electric Power (at time t ) is the product of
potential difference, v
( t
)
, and current, i
( t
)
.
p
( t
) = v
( t
) × i
( t
)
•
Total energy over a time period is calculated by integrating power: w
= t 1 t 2 p
( t
) dt
ELEC176 - Power and Current 2-4
•
To say there is a potential difference of ‘–8 V’ between two nodes is ambiguous without specifying
– which direction of charge movement is defined as positive, and
– which point has the higher electric potential when the potential difference is positive.
•
An arrow, or
+ and
− signs, indicates the direction of a specified potential difference.
This is called the
Reference Polarity.
– Batteries have
+
/
−
(or red/black) marks on their terminals to show polarity.
– The following diagrams indicate the same potential difference:
Node ‘A’
+
+123
V
−
Node ‘B’
Node ‘A’
−
− 123
V
+
Node ‘B’
Positive charge moving from A to B experiences a decrease in potential of 123 V (123 J/C).
ELEC176 - Power and Current 2-5
•
The polarity of a potential difference is also denoted by variable subscripts: e.g.
v
AB
.
Node ‘A’
+ v
AB
−
Node ‘A’
− v
BA
+
Node ‘B’ Node ‘B’
The energy lost by charge Q [C] when it moves from A to B is w
= v
AB
Q
= − v
BA
Q [J].
•
Consider charge Q moving from A to B:
– If v
AB
=
+5 V and Q
=
+2 C, then the energy lost by the charge w
=
+10 J.
– If v
AB
=
–4 V and Q
=
+3 C, then the charge will lose w
=
–12 J. That is, the charge gains energy.
– if w
=
+10 J is added to Q
=
–5 C by whatever moves it, then there will be a potential difference of v
AB
= w
Q
=
+10
− 5
= − 2
V .
A will be at an electric potential of –2 V relative to B, so
B will be at +2 V relative to A, so v
BA
= +2
V.
ELEC176 - Power and Current 2-6
It is common to nominate a reference node called the
common node or the ground node.
v
A
A
+
+ v
AO
− v
AB −
+ v
BO
−
B v
B
O
Relative to the reference node: A has an electric potential of v
AO and B is at an electric potential of v
BO
.
The reference node subscript is often omitted, so it is said that: A is at an electric potential of v
A and B is at an electric potential of v
B
.
The electric potential of A relative to B is v
AB
= v
A
− v
B
ELEC176 - Power and Current 2-7

Current can flow in either direction through a connecting path.
•
An arrow is used to indicate the reference direction of positive current.
i
B
A
If i is negative, the current is simply in the opposite direction to the arrow. The actual direction of charge movement depends on the sign of the charge:
– +ve charge flowing in the direction of the arrow is +ve current ( i >
0
).
– –ve charge flowing in the direction of the arrow is –ve current ( i <
0
).
•
Subscripts can also be used, so that the current from A to B is i
AB and the current from B to A is i
BA
.
i
AB
B
A i
BA or
− i
BA
B
A
ELEC176 - Power and Current 2-8
Current and voltage have direction and this implies that there is also a direction to power.
•
Power can be generated BY something or delivered TO something.
– To indicate this direction of doing work, electric power is not only given a sign
+ or
−
, but is also said to be
generated or absorbed.
– absorbing
− p W is the same as generating
+ p W.
•
Consider the indicated current in the following substance:
A i
AB Substance
+ v
AB
−
B
– i
AB
[C/s] moves from A to B and
– v
AB
[J/C] is subtracted from the charge because the reference direction is from
+ to
− polarity.
Thus the power taken from the current is p
= i
AB v
AB
.
– If p is +ve the substance is absorbing electric power.
– If p is –ve the substance is generating electric power.
ELEC176 - Power and Current 2-9
An electrical device that absorbs electric power is called a Passive Device. Current through a passive device will always result in lost power—electric energy is converted to heat energy in the device.
The common convention is to associate the reference
direction of current and the polarity of potential difference such that: Current reference direction points into the
+ terminal.
i
Device
+ v
−
Then, by this convention, the potential difference and current are associated such that p
= iv is positive when power is taken from the current.
When p >
0
, electric power is dissipated or absorbed by the device — turned into heat, light, motion, etc.
The passive reference configuration is favoured for passive devices, so that the product iv is the electric power absorbed.
ELEC176 - Power and Current 2-10
Consider current from a voltage source through a passive device as follows: i
Voltage Source
+
A
+ v
−
B
Device
•
For the device:
The reference direction of current through it and the polarity of the potential difference across it are in the
Passive Reference Configuration, so electric power dissipated by the device is p
= iv .
This power is generated by the voltage source.
•
For the voltage source:
The reference direction of current is into its
− terminal, so power dissipated by the voltage source is p
S
= − iv .
By convention, the reference direction of electric power generators is into the
− terminal, so that the product iv is the power generated.
ELEC176 - Power and Current 2-11

Consider a conducting substance attached to two nodes, A and B, with a potential difference of v
AB
[V] established by an ideal voltage source, shown here:
+
A
+ i v
AB v
AB
−
B
Substance
•
The electric power absorbed by the substance is p
= i v
AB
.
The reference direction and polarity are in the passive configuration.
•
The electric power generated by the voltage source is p
= i v
AB
.
Note that the reference direction or polarity only suggests that the substance absorbs electric power.
If p <
0
(i.e.
i <
0 or v
AB
<
0
), then the voltage source would be absorbing power supplied by the substance.
ELEC176 - Conduction 3-1
Conduction: The transmission of electricity through a substance by the application of an electric field.
That is, current through a substance due to a potential
difference across it.
Conductivity: The conducting ability of a specified piece of material, in particular a cube of unit dimensions.
That is, the property that determines the current as a function of potential difference for the piece of material.
In general, the conductivity of a device is measured in terms of the number of amps per volt, which is called
conductance.
•
Unit of conductance: siemens (S)
Conductance of one siemens (S) gives a current of one amp per volt (A/V).
ELEC176 - Conduction 3-2
•
A property of all devices is conductance g , which is the change in current that occurs in response to a change in potential difference: g
= di dv
•
In general, g varies with temperature, current, voltage and other factors.
At the end of the process of establishing a potential difference v across a substance, the current through the substance will be i
=
0 v gdv where g , the conductance of the substance, may be a function of v .
•
If g
=
G is constant then i
=
Gv.
ELEC176 - Conduction 3-3 ELEC176 - Conduction
•
Plastics, rubber, dry wood, and dry air are poor conductors ( g
0
.
001
S). Poor conductors are also called insulators — they block the movement of charge.
i
= gv
→ 0 as g
→ 0
.
•
Plastics, ceramics and air are used to isolate circuit nodes from each other. These are insulators with small g . Typically g
10 − 9
S, so the current is much less than
10 − 9
A/V.
•
If there is no connection between two nodes or an insulator between them, then the current from one to the other is nearly zero.
•
The lack of connection between nodes such that i
= 0 is called an open circuit.
3-4

•
Substances that have a large conductivity are called
conductors.
The potential difference across a device, with conductance g , carrying current i is v
= i g
→ 0 for large g.
Zero potential difference implies that the electric potentials at either end of a conductor are the same.
Thus, in most cases, it can be assumed that points connected together by conductors are a single node — the charges at the connected points are at the same potential energy.
•
Electric wires are used to connect together the points of a circuit node. These are conductors made of metals, such as copper, with large g . Typically g
100
S, so the potential difference is much less than
0
.
01
V/A.
•
If there is a wire connecting two nodes, then the potential difference between them is nearly zero.
•
The connection of two nodes such that v
= 0 is called a
short circuit.
ELEC176 - Conduction 3-5 ELEC176 - Conduction
•
Some alloys, carbon and semi-metals (called semiconductors) permit reasonable conduction (
10 − 8
S g
10
S).
These materials are not good conductors, so they present a resistance to current. They absorb electric power from the current as they resist it.
•
The conductance of devices made from some of these materials is nearly constant for all values of current. That is, a plot of i versus v is a straight line.
•
The property of some materials, that ‘current is proportional to potential difference,’ was discovered by
Georg Ohm 1787–1854. He found that v
= i R where R is a constant with units V/A.
Note that the reference direction and polarity are in the passive configuration.
3-6
•
Unit of resistance: ohm (
Ω
)
A resistance of one ohm (
Ω
) is one volt per amp (V/A).
r
= dv di
•
In some devices, v is proportional to i . As Ohm found: v
= iR for some constant R . Then r
= dv
=
R di
For these devices, the resistance is the ratio of v to i , which is the constant R
= v i
.
•
In other devices the relationship between i and v is more complicated.
For example if v
= iF
+
V , then r
= dv di
=
F so r
= v i
.
In these devices, r is often called the dynamic resistance to emphasize that r
= dv di rather than v i
.
ELEC176 - Conduction 3-7
•
Resistors are devices specially constructed to have nearly constant Resistance.
The relationship between current and voltage for a resistor can be modelled by a constant resistance: v i
=
R
That is, the potential difference is proportional to current.
If i is doubled then v is doubled. The electric power absorbed increases four-fold!
The resistance stays fairly constant provided the maximum power rating of the resistor is not exceeded.
•
The relationship between voltage and current for other devices with nearly constant resistance can be modelled in the same way.
That is, the voltage and current for the device are related by a constant resistance.
For the purposes of analysis, it is common to treat these devices as if they were ideal resistors.
ELEC176 - Conduction 3-8

•
Circuit symbol for a resistor:
R R
•
Charge flowing in a resistor will lose energy:
A i
+ v
AB
−
R
B
For a resistor, the relationship between v and i in the passive configuration v
= iR .
Since in the passive configuration v
= iR , then p
= iv
= i
( iR
) = i
2
R and p
= iv
= v v
= v
2
(= v
2
G
)
R R
For any v or i , the electric power absorbed is p
≥ 0
.
The resistor always absorbs power from the current
(transforms it into heat or work).
ELEC176 - Conduction 3-9
• Fundamental Quantities
– Energy: w joule (J).
– Charge: q coulomb (C).
– Power: p watt (W) or (J/s).
p
= dw dt
– Current: i ampere (A) or (C/s).
i
=
– Potential Difference: v dq dt volt (V) or (J/C).
v = dw dq
= p i
•
Voltage and Current
– Potential Difference: polarity, marked
+ and
−
, and value v .
– Current: reference direction, marked by an arrow, and value i .
– Passive configuration: reference direction from
+ to
− inside a device.
– A device absorbs p
= iv where i and v have direction and polarity associated in the passive configuration.
•
Ideal Voltage Source
– v is well defined and is independent of i .
– Power generated: p
= iv where i has a reference direction out of the + terminal (opposite to that of the passive configuration).
•
Conductance and Resistance
– Conductance: g siemens (S) or (A/V) g
=
– Resistance:
•
Ideal Resistor r ohm ( Ω ) or (V/A) r
= dv di di dv
– Constant conductance
– Values of v and i in passive configuration: related by a constant resistance v
= iR .
– Electric power absorbed: p = iv = i
≥ 0
.
2
R = v
2
/R is always
– Good model for many materials and appliances.
ELEC176 - Conduction 3-10