chapter 25 current, resistance and electromotive...
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1
CHAPTER 25
CURRENT, RESISTANCE AND
ELECTROMOTIVE FORCE
BASIC CONCEPTS
CURRENT and CURRENT DENSITY
RESISTANCE and RESISTIVITY
BATTERY INTERNAL RESISTANCE
ENERGY AND POWER IN CIRCUITS
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CURRENT IS THE MOVEMENT OF CHARGE
IN A MATERIAL
In some cases the objects that are moving
are positive.
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In other cases, for example in metals, the
objects are negative (electrons).
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Current is the time rate of passage of the
charge.
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Consider that there are n moving charged
particles per volume
And
The average drift velocity is vd
Then in time dt
The particles move a distance of vddt
In the volume, Avddt, shown in the figure
there will be nAvddt particles.
Each particle has a charge q.
Thus in time dt the charge, dQ, that will
pass through the cylinder is
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Current is
Current density (current per unit cross‐
section of the conductor) is
Note that current density is a vector
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RESISTIVITY
Resistivity, ρ, is a characteristic of a
material.
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RESISTIVITY
Resistivity, ρ, changes with temperature.
Where is the value at 200 C.
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For a metal:
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For Semiconductor:
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Some materials loose all resistivity –
Superconductors:
Discovered in 1911 by H. Kammerlingh
Onnes.
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RESISTANCE
Resistance is a characteristic of an object.
Resistance, R, is related to Resistivity, ρ, by
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The longer the object the higher the
resistance.
The larger the cross‐section the smaller the
resistance.
If ρ is constant the total current through a
conductor is proportional to the voltage
across it.
Or
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The constant of proportionality is the
resistance, R.
Or
This is Ohm’s Law.
If a resistor obeys Ohm’s Law it is an Ohmic
resistor.
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Obeys Ohm’s Law:
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Semiconductors are not Ohmic:
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POWER DISIPATED WITH CURRENT FLOW.
Remember
q
V
Change in energy
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And
Therefore
Use Ohm’s Law
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Or
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CALCULATE RESISTANCE
A copper rod with cross section A has a
length L what is its resistance? Work for
and .
From Table 25.1
Therefore
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More difficult: Example 25.4
A cylinder with resistivity ρ has length L,
inner radius a and outer radius b. Calculate
the resistance for current flow from the
inner to the outer walls.
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Where is the path length of the current
flow.
And is the cross‐section for current flow.
Now
Consider a thin shell within the cylinder wall
with radius , thickness and length .
The area of the shell is .
The path the current flows is .
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Then
Integrate to get .
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CIRCUITS
Circuit elements:
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Other symbols will be added after we
discuss magnetism.
Internal Resistance
Two points:
If no current is in a circuit element there is
no potential drop across the element.
Batteries have internal resistance.
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The figure is of a 12 V battery with no
current in the circuit.
The voltmeter will read 12 V.
But if there is current:
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The voltmeter will read less than 12 V.
What is the current in the circuit?
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What will the voltmeter read?
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