CHAPTER 19: International Trade CHAPTER 19: International Trade.
Chapter 19
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Transcript of Chapter 19
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Chapter 19
A Microscopic View of Electric Circuits
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Steady state and static equilibrium
Static equilibrium: • no charges are moving
Steady state (Dynamic Equilibrium): • charges are moving• their velocities at any location do not change with time• no change in the deposits of excess charge anywhere
Current in a Circuit
In an electric circuit the system does not reach equilibrium!
A microscopic view of electric circuits:• Are charges used up in a circuit?• How is it possible to create and maintain a nonzero electric
field inside a wire?• What is the role of the battery in a circuit?
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IB = IA in a steady state circuit
What is used up in the light bulb?We cannot get something for nothing!
Energy is transformed from one form to another
Electric field – accelerates electronFriction – energy is lost to heatBattery – chemical energy is used up
Closed circuit – energy losses to heat:not an isolated system!
Current in Different Parts of a Circuit
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Momentum principle:
E
Speed of the electron:
Average ‘drift’ speed: - average time betweencollisions
The Drude Model
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Average ‘drift’ speed: - average time betweencollisions
For constant temperature
u – mobility of an electron
Electron current:
The Drude Model
Paul Drude(1863 - 1906)
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In steady state current is the same everywhere in a series circuit.
ii
What is the drift speed?
Note: density of electrons n cannot change if same metal
What is E?
EthickEthin
E and Drift Speed
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2 mm1 mm
1.5.n1 = n2
2.u1 = u2
Every second 1018 electrons enter the thick wire. How many electrons exit from the thin wire every second?
1018
Question
A) 1018
B) 1.5 x 1018
C) 2 x 1018
D) 4 x 1018
E) 12 x 1018
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2 mm1 mm
1.5.n1 = n2
2.u1 = u2
What is the ratio of the electric field, E1/E2?
1018
Question
A) 3:1B) 6:1C) 8:1D) 12:1
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Does current fill the wire? Is E uniform across the wire?
E must be parallel to the wire
E is the same along the wire
0 0VAB VCD
Direction of Electric Field in a Wire
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Connecting a Circuit
The initial transient
When making the final connection in a circuit, feedback forces a rapid rearrangement of the surface charges leading to the steady state.
This period of adjustment before establishing the steady state is called the initial transient.
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1. Static equilibrium: nothing moving(no current)
3. Steady state: constant current (nonzero)
2. Initial transient: short-time processleading to the steady state
Connecting a Circuit
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The current node rule(Kirchhoff node or junction rule [law #1]):
In the steady state, the electron current entering a node in a circuit is equal to the electron current leaving that node
(consequence of conservation of charge)
i1 = i2
i2 = i3 + i4
Current at a Node
Gustav Robert Kirchhoff (1824 - 1887)
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I1 + I4 = I2 + I3
I2 = I1 + I4 - I3 = 3A
I1 + I4 = I2 + I3
I2 = I1 + I4 - I3 = -2A
1ACharge conservation:
Ii > 0 for incomingIi < 0 for outgoing
ExerciseWrite the node equation for this circuit. What is the value of I2?
What is the value of I2 if I4 is 1A?
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Energy conservation (the Kirchhoff loop rule [2nd law]):
V1 + V2 + V3 + … = 0 along any closed path in a circuit
Vwire = ELVbattery = ?
V= U/q energy per unit charge
Energy in a Circuit
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non-Coulomb force on each e
EC
FC
1. FC =eEC
Coulomb force on each e
2. FC =FNC
The function of a battery is to produce and maintain a charge separation.
Energy input per unit chargeemf – electromotive force
The emf is measured in Volts, but it is not a potential difference!The emf is the energy input per unit charge.
chemical, nuclear, gravitational…
Potential Difference Across the Battery
Fully charged battery.
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Round-trip potential difference:
Field and Current in a Simple Circuit
We will neglect the battery’s internal resistance for the time being.
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Round-trip potential difference:
Path 1
Path 2
Field and Current in a Simple Circuit
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The number or length of the connecting wires has little effect on the amount of current in the circuit.
uwires >> ufilament
Work done by a battery goes mostly into energy dissipation in the bulb (heat).
V Across Connecting Wires
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Nichrome wire (resistive)
Twice the Length
Current is halved when increasing the length of the wire by a factor of 2.
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Doubling the Cross-Sectional Area
Nichrome wire
Electron current in the wire increases by a factor of two if the cross-sectional area of the wire doubles.
Loop: emf - EL = 0
𝑖=𝑛𝐴𝑢𝐸
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Two Identical Light Bulbs in Series
Identical light bulbs
Two identical light bulbs in series are the same as one light bulb with twice as long a filament.
The filament lengths add …
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1. Path ABDFA:
2. Path ACDFA:
3. Path ABDCA:
iB = iC
ibatt = 2iB
F
Two Light Bulbs in Parallel
We can think of the two bulbs in parallel as equivalent to increasing the cross-sectional area of one of the bulb filaments.
L … length of bulb filament
The filament areas add …
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The current node rule (Charge conservation)Kirchhoff node or junction rule [1st law]:In the steady state, the electron current entering a node in a circuit is equal to the electron current leaving that node
Analysis of Circuits
V1 + V2 + V3 + … = 0 along any closed path in a circuit
The loop rule (Energy conservation)Kirchhoff loop rule [2nd law]:
V= U/q energy per unit charge
Electron current: i = nAuE Conventional current: I = |q|nAuE