Chapter 1
Introduction to Electricity
for CST 162 LAB
Slide content from “Circuit Analysis: Theory and Practice” 4th Ed., by
Robbins and Miller, 2007
System International (SI)
System of Units
• Electric Current
– Ampere (A)
• Electric Voltage
– Volt (V)
• Electrical Resistance
– Ohm (Ω)
Prefixes
• Metric Prefixes are used for convenience
Significant Digits and
Numerical Accuracy
• Significant digits
– Digits that carry information
– It is a common error to show more digits of
accuracy than are warranted.
Circuit Diagrams
• Electric circuits
– Use batteries and resistors as components
– Circuit diagrams are used on paper
• Three types of circuit diagrams are used
– Pictorial, block, and schematic
Pictorial Diagrams
• Help visualize circuits by showing
components as they actually appear
Block Diagrams
• Blocks represent portions of a system
Schematic
Diagrams
Chapter 2
Voltage and Current
Atomic Theory
• Atom
– Contains a nucleus of protons and neutrons
– Nucleus is surrounded by a group of
orbiting electrons
• Electrons are negative, protons are
positive
Atomic Theory
• Electrically neutral atom
– Equal number of electrons and protons
• Ion
– An atom with an excess or deficit of
electrons
Conductors
• Materials with a large numbers of free
electrons
– Metals are good conductors because they
have few loosely bound valence electrons
Conductors
• Excellent conductors
– Silver
– Gold
– Copper
– Aluminum
Electrical Charge
• Unit of charge is the coulomb (C)
• One coulomb =
6.24 × 1018 electrons (or protons)
• The charge on one electron (or proton) =
1/ 6.24 × 1018 or 1.6 × 10-19 C
Voltage
• When two objects have a difference in
charges
– They have a “potential difference”
or “voltage” between them
• Unit of voltage is the volt
• Thunderclouds
– Millions of volts between them
Voltage
• Difference in potential energy
• Voltage between two points =
One volt, “if it requires one joule of energy to
move one coulomb of charge from one point
to another”
Voltage
• V = Work/Charge
1 joule
1 volt 
1 coulomb
• Voltage is always measured between two points
Current
• Movement of charge is electric current
• More electrons per second passing
through a circuit, the greater the current
• Current is rate of flow of charge
Current
• Unit of current is ampere (A)
• One ampere =
Current in a circuit when one coulomb of charge
passes a given point in one second
• Current = Charge/time
• I = Q/t
Current
• Electron current flow
– Electrons flow from the negative terminal of a
battery to the positive terminal
• Conventional current flow
– We may also assume currents flow from
positive to negative
Current
• Conventional current flow is used in this
course, and in our field of study
How to Measure Voltage
•
•
•
•
Place voltmeter leads across components
Red lead is positive
Black lead is negative
If leads are reversed, you will read the
opposite polarity
How to Measure Current
• Measurable current must pass through
meter
• Open the circuit (i.e. disconnect wires) and
insert the ammeter, so that the current
now flows through the meter
• Connect with correct polarity
Chapter 3
Resistance
Resistance of Conductors
• Resistance of material is dependent on
several factors:
– Type of Material
– Length of the Conductor
– Cross-sectional area
– Temperature
Type of Material
• Atomic differences of materials cause
variations in how electron collisions affect
resistance
• Differences produce resistivity
Length
• Resistance of a conductor
– Directly proportional to its length
– If you double the length of the wire, the
resistance will double
•  = length
– In meters or feet
Area
• Resistance of a conductor
– Inversely proportional to cross-sectional
area of the conductor
• If cross-sectional area is doubled
– Resistance will be one half as much
Fixed Resistors
• Resistance of a fixed resistor is constant
over a wide temperature range
• Rated by amount of resistance
– Measured in ohms (Ω)
• Also rated by power
– Measured in watts (W)
Fixed Resistors
• Different resistors for different applications
– Molded carbon composition
– Carbon film
– Metal film
– Metal Oxide
– Wire-Wound
– Integrated circuit packages
Variable Resistors
• Resistance may be changed (varied)
– Adjust volume, set level of lighting, adjust
temperature
• Have three terminals
– Center terminal connected to wiper arm
• Potentiometers (normally abbreviated to
just “Pot”)
• Rheostats
Color Code
• Colored bands
on a resistor
provide a code
for determining
– Value
– Tolerance
– Reliability
Reading color codes
Measuring Resistance
•
•
•
•
•
•
Use an Ohmmeter
Remove all power sources to circuit
Isolate component to be measured
Connect probes across component
No need to worry about polarity
Ohmmeter determines shorts and opens in
individual components
Chapter 4
Ohm’s Law
and Energy
Ohm’s Law
• Current in a resistive circuit
– Directly proportional to its applied voltage
– Inversely proportional to its resistance
E
I
R
Ohm’s Law
• For a fixed resistance
– Doubling voltage doubles the current
• For a fixed voltage
– Doubling resistance halves the current
Ohm’s Law
• Also expressed as E = IR and R = E/I
• Express all quantities in base units of
volts, ohms, and amps or utilize the
relationship between prefixes
Ohm’s Law in Graphical Form
• Linear relationship between current and
voltage
• y = mx
– y is the current
– x is the voltage
– m is the slope
Ohm’s Law in Graphical Form
• Slope (m) determined by resistor
conductance
Ohm’s Law in Graphical Form
Open Circuits
• Current can only exist where there is a
conductive path
• An “Open circuit” is defined when there
is no conductive path
Open Circuits
• If I = 0
– Ohm’s Law gives R = E/I = E/0  infinity
• An open circuit has infinite resistance
Voltage Symbols
• Voltage sources
– Uppercase E
• Voltage drops
– Uppercase V
• V = I*R
– “IR” drops
Voltage Polarities
• Polarity of voltage drops across resistors is
important in circuit analysis
• Drop is + to – in the direction of conventional
current
• To show this, place plus sign at the tail of
current arrow
Voltage Polarities
Current Direction
• Current usually proceeds out of the
positive terminal of a voltage source
• If the current is actually in this direction, it
will be supplying power to the circuit
Current Direction
• If the current is in the opposite direction
(going into the positive terminal), it will be
absorbing power (like a resistor)
Current Direction
• See two representations of the same current on
next slide
• Notice that a negative current actually proceeds
in a direction opposite to the current arrow
Current Direction
Power Rating of Resistors
• Resistors must be able to safely dissipate
their heat without damage
• Common power ratings of resistors are
1/8, 1/4, 1/2, 1, or 2 watts
Law of Conservation of Energy
• Energy can neither be created nor
destroyed
– Converted from one form to another
• Examples:
– Electric energy into heat
– Mechanical energy into electric energy
Law of Conservation of Energy
• Energy conversions
– Some energy may be dissipated as heat,
giving lower efficiency
Chapter 5
Series Circuits
Series Circuits
• Two elements in a series
– Connected at a single point
– No other current-carrying connections at this
point
• A series circuit is constructed by connecting
various elements in series
Series Circuits
• Normally
– Current will leave the positive terminal of a
voltage source
– Move through the resistor(s)
– Return to negative terminal of the source
Series Circuits
• Current is similar to water flowing through
a pipe
– Current leaving the element must be the
same as the current entering the element
• Same current passes through every
element of a series circuit
Series Circuits
• The laws, theorems, and rules that you
apply to DC circuits
– Also apply to AC circuits
Kirchhoff’s Voltage Law (KVL)
• The algebraic sum of the voltage that rises
and drops around a closed loop is equal to
zero
•
ET - V1 - V2 - V3 - ∙∙∙ - Vn = 0
Kirchhoff’s Voltage Law (KVL)
• Another way of stating KVL is:
– Summation of voltage rises is equal to the
summation of voltage drops around a closed
loop
V1 + V2 + V3 + ∙∙∙ + Vn = ET
Resistors in Series
• Most complicated circuits can be simplified
• For a series circuit
– V1 + V2 + V3 = E
– IR1 + IR2 + IR3 = E
– I(R1 + R2 + R3 )= E
– I(R1 + R2 + R3 )= IRtotal (Note: I’s cancel)
Resistors in Series
• Total resistance in a series circuit is the
sum of all the resistor values
Interchanging Series
Components
• Order of series components
– May be changed without affecting operation of
circuit
• Sources may be interchanged, but their
polarities can not be reversed
• After circuits have been redrawn, it may
become easier to visualize circuit operation
Circuit Ground
• Ground
– Point of reference or a common point in a
circuit for making measurements
• One type of grounding is chassis ground
• In this type of grounding
– Common point of circuit is often the metal
chassis of the piece of equipment
Circuit Ground
• Chassis ground
– Often connected to Earth Ground
• Earth ground
– Physically connected to the earth by a metal
pipe or rod
Circuit Ground
• If a fault occurs within a circuit, the current
is redirected to the earth
• Voltages are often measured with respect
to ground
Ammeter Loading Effects
• An ammeter is placed in a circuit to make
a current measurement
– Resistance in the meter will affect the circuit
• Amount of loading is dependent upon the
instrument and the circuit
Ammeter Loading Effects
• If resistance of the meter is small
compared to the resistance of the circuit,
the loading effect will be small
Chapter 6
Parallel Circuits
Parallel Circuits
• House circuits contain parallel circuits
• The parallel circuit will continue to operate even
though one component may be “open”
• Only the “open” or “defective” component will no
longer continue to operate
• A light bulb with a broken filament = “open”
Parallel Circuits
Parallel Circuits
• Elements in parallel
– When they have exactly two nodes in common
• Elements between nodes
– Any device like resistors, light bulbs, etc.
• Elements connected in parallel
– Same voltage across them
Parallel Circuits
Series - Parallel Circuits
• Circuits may contain a combination of series
and parallel components
• Being able to recognize the various
connections in a network is an important step
in analyzing these circuits
Series - Parallel Circuits
Parallel Circuits
• To analyze a particular circuit
– First identify the node
– Next, label the nodes with a letter or number
– Then, identify types of connections
Parallel Circuits
Kirchhoff’s Current Law (KCL)
• The algebraic sum of the currents entering and
leaving a node is equal to zero
I

0

Kirchhoff’s Current Law (KCL)
• Currents entering the node are taken to be
positive, leaving are taken to be negative
• Sum of currents entering a node is equal to the
sum of currents leaving the node
I  I
in
out
Kirchhoff’s Current Law (KCL)
• An analogy:
– When water flows in a pipe, the amount of
water entering a point is equal to the amount
leaving that point
Resistors in Parallel
• Voltage across all parallel elements in a
circuit will be the same
Resistors in Parallel
• For a circuit with 3 resistors: IT = I1 + I2 + I3
E
E
E
E



RT R1 R2 R3
1
1
1
1



RT R1 R2 R3
Resistors in Parallel
• Total resistance of resistors in parallel will
always be less than resistance of smallest
resistor
Equal Resistors in Parallel
• Total resistance of equal resistors in
parallel is equal to the resistor value
divided by the number of resistors
Two Resistors in Parallel
• For only two resistors connected in parallel, the
equivalent resistance may be found by the
product of the two values divided by the sum
R1R 2
RT 
R1  R 2
• Often referred to as “product over the sum”
formula
Three Resistors in Parallel
• For three resistors in parallel:
R1R 2 R3
RT 
R1R 2  R1R3  R 2 R3
• Rather than memorize this long expression
– Use basic equation for resistors in parallel
Voltmeter Loading Effects
• A voltmeter
– Meter movement in series with a currentlimiting resistance
• If resistance is large compared with the
resistance across which the voltage is to
be measured, the voltmeter will have a
very small loading effect
Voltmeter Loading Effects
• If this resistance is more than 10 times the
resistance across which the voltage is
being measured, the loading effect can
generally be ignored.
• However, it is usually much higher.