Lecture 3:
Electric Currents
Learning Outcomes
After studying the material of this lecture, the student should be able to:
• Explain how a simple battery can produce an electrical current.
• Define current, ampere, emf, voltage, resistance, resistivity, and temperature
coefficient of resistance.
• Distinguish between a) conventional current and electron current and b) direct
current and alternating current.
• Know the symbols used to represent a source of emf, resistor, voltmeter, and
ammeter and how to interpret a simple circuit diagram.
• Given the length, cross sectional area, resistivity, and temperature coefficient of
resistance, determine a wire's resistance at room temperature and some higher
or lower temperature.
• Solve simple dc circuit problems using Ohm's law.
• Use the equations for electric power to determine the power and energy
dissipated in a resistor and calculate the cost of this energy to the consumer.
• Distinguish between the rms and peak values for current and voltage and apply
these concepts in solving problems involving a simple ac circuit.
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Contents of Lecture 3
• The Electric Battery
• Electric Current
• Ohm’s Law: Resistance and Resistors
• Resistivity
• Electric Power
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Contents of Lecture 3
• Power in Household Circuits
• Alternating Current
• Microscopic View of Electric Current
• Superconductivity
• Electrical Conduction in the Human Nervous System
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3-1 The Electric Battery
Volta discovered that electricity could be created if
dissimilar metals were connected by a conductive
solution called an electrolyte.
This is a simple electric cell.
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3-1 The Electric Battery
A battery transforms chemical energy into electrical
energy.
Chemical reactions within the cell create a potential
difference between the terminals by slowly dissolving
them. This potential difference can be maintained even if
a current is kept flowing, until one or the other terminal
is completely dissolved.
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3-1 The Electric Battery
Several cells connected together make a battery,
although now we refer to a single cell as a battery as
well.
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3-2 Electric Current
Electric current is the rate of flow of charge through a
conductor:
(18-1)
Unit of electric current: the ampere, A.
1 A = 1 C/s
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3-2 Electric Current
A complete circuit is one where current can flow all the
way around. Note that the schematic drawing doesn’t
look much like the physical circuit!
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3-2 Electric Current
In order for current to flow, there must be a path from
one battery terminal, through the circuit, and back to the
other battery terminal. Only one of these circuits will
work:
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3-2 Electric Current
By convention, current is defined as flowing from + to –.
Electrons actually flow in the opposite direction, but not
all currents consist of electrons.
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3-3 Ohm’s Law: Resistance and Resistors
Experimentally, it is found that the current in a wire is
proportional to the potential difference between its ends:
IV
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3-3 Ohm’s Law: Resistance and Resistors
The ratio of voltage to current is called the resistance:
(18-2)
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3-3 Ohm’s Law: Resistance and Resistors
In many conductors, the resistance is independent of the
voltage; this relationship is called Ohm’s law. Materials
that do not follow Ohm’s law are called nonohmic.
Unit of resistance:
the ohm, Ω.
1 Ω = 1 V/A
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3-3 Ohm’s Law: Resistance and Resistors
Standard resistors are manufactured for use in electric
circuits; they are color-coded to indicate their value and
precision.
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3-3 Ohm’s Law: Resistance and Resistors
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3-3 Ohm’s Law: Resistance and Resistors
Some clarifications:
• Batteries maintain a (nearly) constant potential
difference; the current varies.
• Resistance is a property of a material or device.
• Current is not a vector but it does have a direction.
• Current and charge do not get used up. Whatever
charge goes in one end of a circuit comes out the other
end.
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3-4 Resistivity
The resistance of a wire is directly proportional to its
length and inversely proportional to its cross-sectional
area:
(18-3)
The constant ρ, the resistivity, is characteristic of the
material.
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3-4 Resistivity
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3-4 Resistivity
For any given material, the resistivity increases with
temperature:
(18-4)
Semiconductors are complex materials, and may have
resistivities that decrease with temperature.
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3-5 Electric Power
Power, as in kinematics, is the energy transformed by a
device per unit time:
(18-5)
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3-5 Electric Power
The unit of power is the watt, W.
For ohmic devices, we can make the substitutions:
(18-6a)
(18-6b)
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3-5 Electric Power
What you pay for on your electric bill is not power, but
energy—the power consumption multiplied by the time.
We have been measuring energy in joules, but the
electric company measures it in kilowatt-hours, kWh.
One kWh = (1000 W)(3600 s) = 3.60 x 106 J
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3-6 Power in Household Circuits
The wires used in homes to carry electricity have very
low resistance. However, if the current is high enough,
the power will increase and the wires can become hot
enough to start a fire.
To avoid this, we use fuses or circuit breakers, which
disconnect when the current goes above a predetermined
value.
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3-6 Power in Household Circuits
Fuses are one-use items—if they blow, the fuse is
destroyed and must be replaced.
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3-6 Power in Household Circuits
Circuit breakers, which are now much more common in
homes than they once were, are switches that will open if
the current is too high; they can then be reset.
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3-7 Alternating Current
Current from a battery
flows steadily in one
direction (direct current,
DC). Current from a power
plant varies sinusoidally
(alternating current, AC).
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3-7 Alternating Current
The voltage varies sinusoidally with time:
(18-7a)
as does the current:
(18-7b)
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3-7 Alternating Current
Multiplying the current and the voltage gives the power:
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3-7 Alternating Current
Usually we are interested in the average power:
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Summary of Lecture 3
• A battery is a source of constant potential difference.
• Electric current is the rate of flow of electric charge.
• Conventional current is in the direction that positive
charge would flow.
• Resistance is the ratio of voltage to current:
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Summary of Lecture 3
• Ohmic materials have constant resistance, independent
of voltage.
• Resistance is determined by shape and material:
• ρ is the resistivity.
• Power in an electric circuit:
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Summary of Lecture 3
• Direct current is constant
• :AC Current varies sinusoidally.
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