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Electrical Current
By: Señor Sheinkopf
Electrical Current
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Electric current is the rate at which charge
passes a given point in a circuit
An electrical circuit is a closed path along
which charged particles move
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A switch is a device for making, breaking, or
changing the connections in an electrical circuit
The symbol for a switch is:
Current
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The unit for electrical current is the Ampere
(A)
Current is a function of the change in charge
over a unit of time
I = ∆q/t
Where I is the current in amperes, q is the charge
in coulombs, and t is the time in seconds
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We can use an ammeter to measure current in
an electrical appliance
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An ammeter is a device that measures electrical
current
The symbol for an ammeter is:
Conditions Necessary for an Electric
Current
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In addition to a complete circuit, a difference in
potential between two points in the circuit must exist
for there to be an electric current
The potential difference may be supplied by:
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A cell – a device that converts chemical energy to electrical
energy
Or a battery – a combination of two or more
electrochemical cells
The potential difference may be measured with a device
called a voltmeter.
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These devices are represented in an electric
circuit diagram by the following symbols:
Cell
Battery
Voltmeter
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Positive charges tend to move from points of
higher potential to points of lower potential
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Or, from positive potential to negative potential
Negative charges tend to move in the opposite
direction
We call the current flow from positive to
negative, conventional current
The electron flow, however, goes from the negative
terminal to the positive
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Current
Electrical Power
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The energy carried by an electric current is
related to the voltage, E = qV
Since current, I = q/t, is the rate of charge flow,
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The power, P = E/t, of an electric device can be
determined by multiplying voltage and current
P = IV
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Power is equal to the current times the potential
difference (i.e. voltage)
The unit for power will still remain the watt (W)
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Power is the rate at which energy is delivered or
changed from one form to another
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i.e. electric energy to mechanical energy in motors,
electrical to light in lightbulbs
Question
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If the current through a motor is 3.0 A and the
potential difference is 120 V,
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What is the power in the motor?
P = IV = (3.0 A) * (120 V) = 360 W
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Suppose there is a potential difference between
two pieces of metal
If those pieces of metal are connected by a copper
rod, a large current is created
 If those pieces of metal are connected by a glass
rod, almost no current is created
 Why?
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The property determining how much current
will flow is called resistance.
Resistance
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Resistance is measured by placing a potential
difference across a conductor and dividing the
voltage by the current
R = V/I
where R is the resistance, V is the potential
difference (voltage), and I is the current
Factors that Affect Resistance
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The resistance of a wire, R, varies directly with
the length of the wire, L
The resistance of a wire, R, varies indirectly with
the cross-sectional area of the wire, A
Resistivity, ρ, a measure of resistance in a
particular substance
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Depends on the electronic structure and the
temperature of the material
R = ρ L/A
The unit for resistivity is the ohm·meter
Ohm’s Law
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The resistance of the conductor, R is measured
in ohms.
Ohm ~ Ω
One ohm (1 Ω) is the resistance permitting an
electric charge of 1 A to flow when a potential
difference of 1 V is applied across the
resistance.
The equation R = V/I is also known as
Ohm’s Law
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Ohm’s Law shows that as long as the electrical circuit is
at constant temperature (no heat is being generated),
the ratio of potential difference to current is constant
for a given conductor
The resistance for most conductors do not vary as the
magnitude or direction of the potential applied to it
changes
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Some important devices, however, do not obey this law.
Devices that contain many transistors and diodes, like your
calculator
Even a light bulb has resistance that depends on its
temperature and thus does not obey Ohm’s Law
Resistors
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Wires used to connect electric devices have low
resistance.
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Wires used in home wiring can have a resistance as low as
0.004 Ω
Because wires have so little resistance, there is almost
no potential drop across them.
To produce greater potential drops, a large resistance
concentrated into a small volume is necessary
A resistor is a device designed to have a specific
resistance
 Resistor
The color bands represent a code for the value of resistance
each resistor possesses
•The first three bands each give a value for the resistance
•The last band give a percent of give-or-take for the resistance
which depends on the temperature of the resistor at any given
moment
COLOR
1st BAND
2nd BAND
3rd BAND
MULTIPLIER TOLERANCE
Black
0
0
0
1Ω
Brown
1
1
1
10 Ω
±1%
Red
2
2
2
100 Ω
±2%
Orange
3
3
3
1 KΩ
Yellow
4
4
4
10 KΩ
Green
5
5
5
100 KΩ
±0.5%
Blue
6
6
6
1 MΩ
±0.25%
Violet
7
7
7
10 MΩ
±0.10%
Grey
8
8
8
White
9
9
9
±0.05%
Gold
0.1 Ω
±5%
Silver
0.01 Ω
±10%
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So this resistor would have a value of 2 (red), 6
(blue), 5 (green), and +/- 5% (gold)
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We would read this as a resistor having 265 Ω of
resistance, plus or minus 5%
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The symbol we use on our circuit diagrams for
resistors is the following:
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Ohm’s Law applet
Question
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A sensor uses 2.0x10-4 A of current when it is
operated by a 3.0 V battery. What is the
resistance of the sensor circuit?
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R = V/I = (3.0 V) / (2.0x10-4 A) = 1.5x104 Ω
Questions
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A 75 W lamp is connected to 125 V.
What is the current through the lamp?
 P = IV  75 W = I (125 V)  I = 0.6 A
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What is the resistance of the lamp?
 R = V/I = (125 V) / (0.6 A) = 208.3 Ω
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Superconductors
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A superconductor is a material with zero
resistance
There is no restriction of current so there is no
potential difference, V, across them
Because there is no resistance, superconductors
can conduct electricity without loss of energy
At present, however, all superconductors must
be kept at temperatures below 100 K
A practical use for superconductors include MRI
magnets
Parallel Connection
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When a voltmeter is connected across another
component, it is called a parallel connection
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The circuit component and the voltmeter are aligned
parallel to each other in the circuit
Any time the current has two or more paths to
follow, the connection is labeled parallel
Series Connection
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An ammeter measures the current through a
circuit component.
The same current going through the component
must go through the ammeter, so there can be
only one current path.
A connection with only one current path is
called a series connection
In a series connection, there can be only a single
path through the connection
Ohm’s Law and Power
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Knowing Ohm’s Law we can find new ways to
calculate the electrical power present
If you know I and R:
P = IV and V = IR (Ohm’s Law)
Substituting we get, P = I (I R) = I2R
 so:
P = I2R
 This means that the power dissipated in a resistor is
proportional both to
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the square of the current passing through it
 as well as to the resistance
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If you know V and R but not I:
P = IV and I = V/R (Ohm’s Law)
Substituting we get, P = ( V/R ) * V
 So:
P = V2/R
 This means that electrical power is equal to the
voltage squared divided by the resistance
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The Kilowatt-hour
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While electric companies are often called power
companies, the actually provide energy rather
than power.
The joule, also defined as a watt-second, is a
relatively small amount of energy, too small for
commercial sales use
Therefore, electric companies measure their
energy sales in a unit called the kilowatt-hour
A kilowatt-hour is equivalent to 3.6x106J
The Electrovolt
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An important connotation to know, at least with
electrical energy is the idea of the electrovolt
If an elementary charge is moved against an electric
field through a potential difference of one volt, the
work done on the charge is calculated as:
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W = Vq = (1.0 V) * (1.60x10-19C) = 1.60 x10-19 J
This amount of work, or gain in potential energy, is
called the electrovolt, eV.
1 eV = 1.60x10-19J
Circuits
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There are three types of circuit connections
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Series
 Parallel
And a combination of both Series and Parallel
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Series Circuit
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Since there is only one current path in a series
circuit, the current is the same through each
resistor.
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For resistors in series, the current is given by
I = I1 = I2 = I3 = ....
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The applied potential difference at the terminals
equals the sum of the potential differences
across the individual resistors.
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For resistors in series, the potential difference
(voltage) is given by
V = V1 + V2 + V3 + ….
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However, by Ohm’s Law, V = IReq
Where Req is the equivalent resistance of the entire
circuit
 Equivalent Resistance is the single resistance that
could replace the several resistors in a circuit.
 Substituting yields:
V = IReq = I1R1 + I2R2 + I3R3 + ….
However since I = I1 = I2 = I3 = ...., we can follow with

IReq = IR1 + IR2 + IR3 + ….
And if we divide everything by the common I,
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We get, for the equivalent resistance,
Req = R1 + R2 + R3 + ….
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To summarize for series circuits:
I = I1 = I2 = I3 = ....
V = V1 + V2 + V3 + ….
Req = R1 + R2 + R3 + ….
Parallel Circuit
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In a parallel circuit, the sum of the currents in
the branches is equal to the total current from
the source.
That is,
I = I1 + I2 + I3 + ....
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The potential difference (voltage) across each
branch of the parallel circuit is the same as that
of the potential difference supplied by the
source, so
V = V1 = V2 = V3 = ….
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However, according to Ohm’s Law, I = V/R for each
branch of the circuit
V1 V2 V3
I 
  ....
R1 R2 R3
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And since I = V/Req,
V
V V V
 
  ....
Req R1 R2 R3
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Dividing each term by the voltage, V, yields
For the equivalent resistance in a
parallel circuit:
1
1
1
1
 
  ....
Req R1 R2 R3
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To summarize for parallel circuits:
I = I1 + I2 + I3 + ....
V = V1 = V2 = V3 = ….
1 /Req = 1/R1 + 1/R2 + 1/R3 + ….
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If we have a mixed circuit,
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We need to first simplify our parallel components into a
resulting ‘singular’ component that is in series with the
rest of the circuit.
Then we can combine our components as if it were all
in series
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So we want to combine R2 and R3 and find the
Req for those two in parallel
Then take that Req and combine it with R1 in
series to find a new final equivalent resistance
The same theory applies to finding the current
and/or voltage throughout the circuit