Voltage, Current and Resistance

Outline
• Atoms
• Electrical Charge
• Voltage
• Current
• Resistance
• The Electric Circuit
• Basic Circuit Measurements

4
Atoms

• Electrically balanced at
normal state

Figure: Bohr’s model of an atom

5
Atoms
• “Outermost shell”
– Valence shell
• “Electrons in valence shell”
– Valence electrons

• “Electron that escapes from

the atom because of a
photon of sufficient energy”
– Free electron
Figure: Shells and energy levels
• “An atom with a net charge”
– An ion

6
Categories

Conductors Semiconductors Insulators

• Materials that • Fewer free • Nonmetallic

readily allow electrons than materials
current conductors • Glass, porcelain,
• Silver, Copper • Four valence Teflon,
electrons polyethylene
• Silicon,
Germanium

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Electrical Charge
• “An electrical property of
matter that exists because of
an excess or deficiency of
electrons”
– Electrical charge, Q Figure: Electric field between two
oppositely charged surfaces

Figure: Attraction and repulsion of electrical charges

8
Electrical Charge
• Electrical charge is measured 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 𝑜𝑜𝑜𝑜 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒
in coulombs, C. Total charge, 𝑄𝑄 =
6.25×1018 𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒/𝐶𝐶

• One coulomb is the total

charge possessed by
6.25 × 1018 electrons.

• A single electron has a charge

of 1.6 × 10−19 C.

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Voltage
• “Energy per unit of charge”
𝑊𝑊
– Voltage 𝑉𝑉 =
𝑄𝑄

where V is voltage in volts (V),

• “The potential difference W is energy in joules (J),
(voltage) between two points
Q is charge in coulombs (C).
when one joule of energy is
used to move one coulomb of
charge from one point to the
other.” – One volt
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Voltage
• Produced by means of
chemical energy, light energy,
and magnetic energy
combined with mechanical
motion

Figure: Voltage source graph

Figure: Symbol of dc voltage sources

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Current

• “Movement of electrons”
– Current Figure: Random motion of free electrons

Figure: Electrons flow when voltage is applied

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Current
• “The rate of flow of charge” 𝑄𝑄
– Electrical current, I 𝐼𝐼 =
𝑡𝑡

where I is current in amperes (A)

• Measured by the number of Q is the charge of electrons
electrons (amount of charge) in coulombs (C)
that flow past a point in a t is time in seconds (s)
unit of time

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Current

• “The amount of current that

exists when a number of
electrons having a total
Figure: Illustration of 1 A of current
charge of one coulomb (1 C)
move through a given cross-
sectional area in one second
(1 s)” – One ampere (1A)
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Current

Figure: Symbol of current source Figure: IV characteristic graph

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Resistance
• “The opposition to current”
– Resistance, R
Figure: Symbol of resistance

• “Resistance that exists when

there is one ampere (1 A) of
current in a material with one
volt (1 V) applied across the
material” – One ohm (1 Ω).
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Resistance

• “The reciprocal of resistance” 1

– Conductance, G 𝐺𝐺 =
𝑅𝑅

• Unit of conductance is
siemens, S.

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Resistors
• “Components that
are designed to have
a certain amount of
resistance”
– Resistors

Figure: Typical fixed resistors

• Two types: fixed or
variable

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Resistors

Figure: Two types of fixed resistors

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Resistors

Figure: Typical film resistors Figure: Typical wirewound power resistors

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Resistor Color Codes

Figure: 4-band resistor

Table: 4-band resistor color code 21

Resistor Color Code

Figure: 5-band resistor

Table: 5-band resistor color code 22

 Resistor Label Code

Figure: Three-digit labeling for a resistor Figure: Alphanumeric resistor label

• Labels for resistance tolerance for one system:

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Variable Resistors

• “The variable resistor

used to divide voltage”
– Potentiometer

Figure: Symbols of potentiometer and rheostat

• “The variable resistor

used to control current”
– Rheostat

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Variable Resistors

Figure: Typical potentiometers and construction views

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Variable Resistors

• Linear potentiometer • Tapered potentiometer

Figure: Linear potentiometer Figure: Tapered potentiometer

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Variable Resistance Sensors

Photoconductive
Thermistors Strain gauges
cells
• Function of • Function of • Function of
temperature light force

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The Electric Circuit

• Circuit: Voltage source,

Load, Path for current

Figure: Simple electric circuit

• Load: A device on which
work is done by the current
through it

Figure: Schematic for electric circuit

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Open Circuit and Close Circuit
• Closed circuit: • Open circuit: Broken
Complete current path current path

• Switch: Control opening and closing of circuits

• Pole: Movable arm in a switch
• Throw: The number of contacts affected by a single switch
action (single movement of a pole)
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Types of Switches
Single-pole- Normally open
single-throw push-button
(SPST) (NOPB)

Single-pole- Normally
double-throw closed push-
(SPDT) button (NCPB)

Double-pole- Single-pole
single-throw rotary
(DPST) (6-position)

Double-pole-
double-throw
(DPDT)

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Types of Switches

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Protective Devices
• Fuses and circuit breakers
• Deliberately create an open circuit
• Two types of fuses: fast-acting and time-
delay (slow blow)
• Slow blow fuses: Greater and longer Figure: Bimetallic spring
duration surges of current
• Circuit breakers: Detect heating effect or
magnetic field
• Heating effect: bimetallic spring opens
the contact
http://www.shivalikbimetals.com/images/product/main/1_1200055689_spring.jpg
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Protective Devices

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Wires
• American Wire Gauge (AWG)
number
𝐴𝐴 = 𝑑𝑑 2
• Gauge number increases, wire
diameter decreases where A is the cross-sectional area in
circular mils (CM),
d is the diameter in mils (0.001 in
or 1 mil)

Figure: cross-sectional area of a wire

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Wires

Table: AWG sizes and resistance values for solid round copper 35
Wire Resistance

Depends on 𝜌𝜌𝜌𝜌
• Type of material 𝑅𝑅 =
𝐴𝐴
• Length of wire
• Cross-sectional area where R is the resistance in ohms
• Heat 𝜌𝜌 is the resistivity in CM-Ω/ft
𝑙𝑙 is the length in feet
A is the cross-sectional area
in circular mils

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Wires

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Ground
• The reference point in an electric circuit
• Earth ground: an 8-foot metal rod driven
into the earth Figure: Earth ground or reference ground
• Green or bare copper wire in household
wiring
• Normally connected to the metal chassis
of an appliance or a metal electrical box
Figure: Chassis ground
• Reference ground/Common (COM or
COMM): represents a common
conductor
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Measuring Current & Voltage

• Connect an ammeter in the • Connect a voltmeter in

current path in series parallel connection across
connection the component

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Summary
• Voltage is energy per unit charge. Voltage shows the potential
difference between two points. Unit is volt (V).
• Current is the rate of flow of charge. Unit is ampere (A).
• Resistance is the opposition to current. Unit is ohm (Ω).
• A basic electric circuit consists of source, load and current path
between source and load.
• Ground is the reference point with zero voltage with respect to other
points.
• Ammeter is connected in series in the current path.
• Voltmeter is connected in parallel across the component.
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Next
• Ohm’s law, energy and power

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Series Circuits
Outline
• Resistors in Series
• Total Series Resistance
• Current in a Series Circuit
• Application of Ohm’s Law
• Voltage Sources in Series
• Kirchhoff’s Voltage Law
• Voltage Dividers
• Power in Series Circuits
• Voltage Measurements

4
Resistors in Series

• A series circuit provides only

one path for current between
two points.

• The current is the same

through each series resistor.
Figure: Resistors in series form a string

5
Total Series Resistance
• For every resistor added in series, the total resistance increases.

𝑅𝑅𝑇𝑇 = 𝑅𝑅1 + 𝑅𝑅2 + 𝑅𝑅3 + ⋯ + 𝑅𝑅𝑛𝑛

where RT is the total resistance, and

Rn is the last resistor in the series string.

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Total Series Resistance

7
Total Series Resistance

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Equal-Value Series Resistors
• For more than one resistor of the same value in series,

𝑅𝑅𝑛𝑛 = 𝑛𝑛𝑛𝑛

where n is the number of equal-value resistors, and

R is the resistance value.

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Current in a Series Circuit
• The current is the same through all points in a series circuit.

Figure: Current values at the entrance point and exit point are the same

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Application of Ohm’s Law

𝑉𝑉𝑇𝑇
Same polarity 𝐼𝐼𝑇𝑇 =
𝑅𝑅𝑇𝑇
+

VT Vx Rx 𝑉𝑉𝑥𝑥
𝐼𝐼𝑇𝑇 =
IT − 𝑅𝑅𝑥𝑥

𝑉𝑉𝑥𝑥 = 𝐼𝐼𝑇𝑇 𝑅𝑅𝑥𝑥

An open in a series circuit prevents current; therefore,

there is zero voltage drop across each series resistor.
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Application of Ohm’s Law

12
Application of Ohm’s Law

13
Application of Ohm’s Law

14
Application of Ohm’s Law

15
Voltage Sources in Series

• Series-aiding arrangement
• Series voltage sources are added
when their polarities are in the same
direction.

• Series-opposing arrangement
• Series voltage sources are subtracted
when their polarities are in the
opposite direction.
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Voltage Sources in Series

17
Voltage Sources in Series

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Kirchhoff’s Voltage Law (KVL)
“The sum of all the voltage drops
around a single closed path in a circuit
is equal to the total source voltage in
that closed path.”

𝑉𝑉𝑆𝑆 = 𝑉𝑉1 + 𝑉𝑉2 + 𝑉𝑉3 + ⋯ + 𝑉𝑉𝑛𝑛

where subscript 𝑛𝑛 represents the number of voltage drops.

Figure: Sum of n voltage drops
equals the source voltage
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 Kirchhoff’s Voltage Law (KVL)
Voltage drop

“The algebraic sum of the voltages

around any closed path in a circuit
Voltage rise
is equal to zero.”

𝑉𝑉1 + 𝑉𝑉2 + 𝑉𝑉3 + ⋯ + 𝑉𝑉𝑛𝑛 = 0

Figure: Sum of n voltage drops

equals the source voltage
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Kirchhoff’s Voltage Law (KVL)

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Kirchhoff’s Voltage Law (KVL)

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Voltage Dividers
• “A circuit consisting of a series string of resistors connected to a
voltage source acts as a voltage divider”.
By Ohm’s Law,
𝑉𝑉𝑆𝑆
𝑉𝑉𝑥𝑥 = 𝐼𝐼𝑅𝑅𝑥𝑥 , where𝐼𝐼 =
𝑅𝑅𝑇𝑇
𝑅𝑅𝑇𝑇 = 𝑅𝑅1 + 𝑅𝑅2 + 𝑅𝑅3 + ⋯ + 𝑅𝑅𝑛𝑛
Then,
𝑉𝑉𝑆𝑆
𝑉𝑉𝑥𝑥 = 𝑅𝑅
𝑅𝑅𝑇𝑇 𝑥𝑥

𝑅𝑅𝑥𝑥
𝑉𝑉𝑥𝑥 = 𝑉𝑉𝑆𝑆
𝑅𝑅𝑇𝑇
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Voltage Dividers

24
The Potentiometer as an Adjustable Voltage
Divider

25
The Potentiometer as a Volume Control

26
The Potentiometer as a Level Indicator

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Conversion of Sensor Resistance to a Voltage

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Power in Series Circuit

“The total amount of power 𝑃𝑃𝑇𝑇 = 𝑃𝑃1 + 𝑃𝑃2 + 𝑃𝑃3 + ⋯ + 𝑃𝑃𝑛𝑛

in a series resistive circuit is where 𝑃𝑃𝑇𝑇 is the total power, and
𝑃𝑃𝑛𝑛 is the power in the last resistor in series.
equal to the sum of the
powers in each resistor in 𝑉𝑉𝑆𝑆2
𝑃𝑃𝑇𝑇 = 𝑉𝑉𝑆𝑆 𝐼𝐼 𝑃𝑃𝑇𝑇 = 𝐼𝐼 2 𝑅𝑅𝑇𝑇 𝑃𝑃𝑇𝑇 =
𝑅𝑅𝑇𝑇
series.”

29
Power in Series Circuit

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Voltage Measurements
“In electronic systems, reference ground (or common) refers
to a conductor that is the comparison point for voltage
measurements in a circuit.”

(a) Positive voltages (b) Negative voltages (c) Positive and negative voltages

Figure: (a) (b) (c) with respect to ground

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Voltage Measurements

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Summary
• The total resistance between any two points in a series circuit is equal to
the sum of all resistors connected in series between those two points.
• The current is the same at all points in a series circuit.
• Voltage sources in series add algebraically.
• Kirchhoff’s voltage law: The sum of the voltage drops in a series circuit
equals the total source voltage.
• Kirchhoff’s voltage law: the algebraic sum of all the voltages around a
closed single path is zero.
• A voltage divider is a series arrangement of resistors connected to a voltage
source.
• A potentiometer can be used as an adjustable voltage divider.

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Summary
• The total power in a resistive circuit is the sum of all the individual
powers of the resistors making up the series circuit.
• Voltages given with a single-lettered subscript are referenced to
ground. When two different letters are used in the subscript, the
voltage is the difference in the two points.
• Ground (common) is zero volts with respect to all points referenced
to it in the circuit.
• Negative ground is the term used when the negative side of the
source is grounded.
• Positive ground is the term used when the positive side of the source
is grounded.

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Next
• Parallel Circuits

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