Announcements
Review
Electric Current
Electric Currents
Sections 18.1 - 18.3
Electric Currents
Resistance
Final Questions
Announcements
Review
Electric Current
Resistance
Reading Assignment
Read sections 18.4 - 18.6
Homework Assignment 2
Homework for Chapter 17 is due in class today
Homework Assignment 3
Homework for Chapter 18 (due at the beginning of class on Wednesday, September 15)
Q: 6, 9, 11, 13, 18
P: 6, 10, 14, 32, 82
Electric Currents
Final Questions
Announcements
Review
Electric Current
Resistance
Final Questions
Capacitance
The capacitance C of a capacitor is defined as the ratio of the magnitude of the charge on either conductor to the
magnitude of the potential difference between the conductors
C ≡
Q
∆V
Capacitance is always a positive quantity (Q and ∆V are expressed as positive quantities)
The SI unit of capacitance is the farad (1 F = 1 C/V)
Typically, capacitances range from microfarads (10−6 F) to picofarads (10−12 F)
Capacitance depends only on the geometry of the capacitor (the shape and separation of the conductors)
Electric Currents
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Electric Current
Resistance
Final Questions
Capacitance
The capacitance C of a capacitor is defined as the ratio of the magnitude of the charge on either conductor to the
magnitude of the potential difference between the conductors
C ≡
Q
∆V
Capacitance is always a positive quantity (Q and ∆V are expressed as positive quantities)
The SI unit of capacitance is the farad (1 F = 1 C/V)
Typically, capacitances range from microfarads (10−6 F) to picofarads (10−12 F)
Capacitance depends only on the geometry of the capacitor (the shape and separation of the conductors)
Energy stored by a capacitor
The energy stored in a charged capacitor is
U =
Q2
2C
=
1
2
QV =
1
2
CV
2
This result is independent of the geometry of the capacitor!
We can imagine the energy stored in a capacitor to be stored in the electric field created between the
charged plates
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Electric Current
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Final Questions
Current
Current is the rate at which charge flows through a surface
If ∆Q is the amount of charge that passes through a surface in a time interval ∆t, average current Iavg is
Iavg =
The instantaneous current I is defined as
I =
The SI unit of current is the ampere (1 A = 1 C/s)
Electric Currents
∆Q
∆t
dQ
dt
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Final Questions
Current
Current is the rate at which charge flows through a surface
If ∆Q is the amount of charge that passes through a surface in a time interval ∆t, average current Iavg is
Iavg =
The instantaneous current I is defined as
I =
∆Q
∆t
dQ
dt
The SI unit of current is the ampere (1 A = 1 C/s)
Convention
A current arrow is drawn in the direction in which positive charge carriers would move, even if the actual
charge carriers are negative and move in the opposite direction
The direction of (positive) current is from high potential (+) toward low potential (-)
In electrical conductors, it is the negatively charged electrons that are allowed to move
Therefore, in an ordinary conductor, the direction of the current is opposite the direction of flow of
electrons
Electric Currents
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Electric Current
Question
If a conducting wire is connected in a loop, what will happen?
Electric Currents
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Final Questions
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Electric Current
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Final Questions
Question
If a conducting wire is connected in a loop, what will happen?
Answer
Since all points inside the conducting wire are at the same electric potential, there is no electric field inside
the wire
With zero electric field, there is no net transport of charge inside the wire, so there is no current
Electric Currents
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Electric Current
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Final Questions
Question
If a conducting wire is connected in a loop, what will happen?
Answer
Since all points inside the conducting wire are at the same electric potential, there is no electric field inside
the wire
With zero electric field, there is no net transport of charge inside the wire, so there is no current
Question
If the ends of the wire are connected to a battery, what will happen?
Electric Currents
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Electric Current
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Final Questions
Question
If a conducting wire is connected in a loop, what will happen?
Answer
Since all points inside the conducting wire are at the same electric potential, there is no electric field inside
the wire
With zero electric field, there is no net transport of charge inside the wire, so there is no current
Question
If the ends of the wire are connected to a battery, what will happen?
Answer
The battery sets up a potential difference between the ends of the loop, which creates an electric field
within the wire
This electric field exerts forces on the electrons inside the wire, creating a current
Electric Currents
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Electric Current
Resistance
Final Questions
Drift speed
When a conductor does not have a current through it, its conduction electrons move randomly, with no net
motion in any direction
When the conductor does have a current through it, these electrons still move randomly, but now they
tend to drift with a drift speed vd in the direction opposite that of the applied electric field
The drift speed is tiny compared to the speeds in the random motion
In a typical metallic conductor, the random motion speeds of the electrons are around 106 m/s
In a typical metallic conductor, the drift speeds are around 10−7 to 10−4 m/s
Electric Currents
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Electric Currents
Review
Electric Current
Resistance
Final Questions
Announcements
Review
Electric Current
Resistance
Final Questions
Drift speed
When a conductor does not have a current through it, its conduction electrons move randomly, with no net
motion in any direction
When the conductor does have a current through it, these electrons still move randomly, but now they
tend to drift with a drift speed vd in the direction opposite that of the applied electric field
The drift speed is tiny compared to the speeds in the random motion
In a typical metallic conductor, the random motion speeds of the electrons are around 106 m/s
In a typical metallic conductor, the drift speeds are around 10−7 to 10−4 m/s
Question
If the drift speed of electrons in a conductor is so small, why does it not take several hours for appliances to “turn
on”?
Electric Currents
Announcements
Review
Electric Current
Resistance
Final Questions
Drift speed
When a conductor does not have a current through it, its conduction electrons move randomly, with no net
motion in any direction
When the conductor does have a current through it, these electrons still move randomly, but now they
tend to drift with a drift speed vd in the direction opposite that of the applied electric field
The drift speed is tiny compared to the speeds in the random motion
In a typical metallic conductor, the random motion speeds of the electrons are around 106 m/s
In a typical metallic conductor, the drift speeds are around 10−7 to 10−4 m/s
Question
If the drift speed of electrons in a conductor is so small, why does it not take several hours for appliances to “turn
on”?
Answer
The conductor is filled with electrons so we do not have to wait for an electron to travel its full length
Electric Currents
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Electric Current
Resistance
Final Questions
Resistance
Resistance is defined as the ratio of the potential difference across a conductor to the current in the
conductor
∆V
R ≡
I
The SI unit of resistance is the ohm (1 Ω = 1 V/A)
Electric Currents
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Electric Current
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Final Questions
Resistance
Resistance is defined as the ratio of the potential difference across a conductor to the current in the
conductor
∆V
R ≡
I
The SI unit of resistance is the ohm (1 Ω = 1 V/A)
Ohm’s law
A conducting device obeys Ohm’s law when the resistance of the device is independent of the magnitude
and polarity of the applied potential difference
Materials that obey Ohm’s law are said to be ohmic
Electric Currents
Announcements
Electric Currents
Review
Electric Current
Resistance
Final Questions
Announcements
Review
Electric Current
Resistance
Final Questions
Resistance
Resistance is defined as the ratio of the potential difference across a conductor to the current in the
conductor
∆V
R ≡
I
The SI unit of resistance is the ohm (1 Ω = 1 V/A)
Ohm’s law
A conducting device obeys Ohm’s law when the resistance of the device is independent of the magnitude
and polarity of the applied potential difference
Materials that obey Ohm’s law are said to be ohmic
Resistors
A resistor is an electronic component that impedes the flow of electric current, converting some of its
energy into heat
When charge flows through a resistor, it experiences a drop in electric potential given by
∆V = IR
Electric Currents
Announcements
Review
Electric Current
Resistance
Reading Assignment
Read sections 18.4 - 18.6
Homework Assignment 2
Homework for Chapter 17 is due in class today
Homework Assignment 3
Homework for Chapter 18 (due at the beginning of class on Wednesday, September 15)
Q: 6, 9, 11, 13, 18
P: 6, 10, 14, 32, 82
Electric Currents
Final Questions