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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

CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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Page 1: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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 

Page 2: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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CURRENT IS THE MOVEMENT OF CHARGE 

IN A MATERIAL 

 

 

In some cases the objects that are moving 

are positive. 

 

Page 3: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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In other cases, for example in metals, the 

objects are negative (electrons). 

 

  

 

Page 4: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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Current is the time rate of passage of the 

charge. 

 

 

 

 

Page 5: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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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 

Page 6: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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Current is        

 

Current density (current per unit cross‐

section of the conductor) is 

 

 

 

Note that current density is a vector  

 

 

 

Page 7: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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RESISTIVITY 

 

Resistivity, ρ, is a characteristic of a 

material. 

 

 

 

 

 

Page 8: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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RESISTIVITY 

Resistivity, ρ, changes with temperature.  

 

 

 

Where   is the value at 200 C. 

 

 

 

 

 

Page 9: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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For a metal: 

 

 

 

 

 

 

Page 10: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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For Semiconductor: 

 

 

 

 

 

 

 

Page 11: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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Some materials loose all resistivity – 

Superconductors: 

 

 

Discovered in 1911 by H. Kammerlingh 

Onnes. 

Page 12: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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RESISTANCE 

Resistance is a characteristic of an object. 

Resistance, R, is related to Resistivity, ρ, by 

 

 

 

Page 13: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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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 

 

 

 

Page 14: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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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. 

 

 

Page 15: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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Obeys Ohm’s Law: 

 

 

 

Page 16: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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Semiconductors are not Ohmic: 

 

 

 

 

Page 17: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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POWER DISIPATED WITH CURRENT FLOW. 

 

Remember 

 

                  

        q     

             

 

         V 

Change in energy   

 

 

 

 

Page 18: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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And       

 

Therefore   

 

Use Ohm’s Law 

 

 

Page 19: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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Or                 

 

          

             

 

   

Page 20: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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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 

 

 

 

 

 

Page 21: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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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. 

 

 

 

 

 

Page 22: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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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  . 

Page 23: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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Then 

 

 

Integrate to get  . 

 

 

 

 

 

 

 

Page 24: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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CIRCUITS 

 

Circuit elements: 

 

 

Page 25: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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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. 

 

 

Page 26: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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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: 

 

Page 27: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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The voltmeter will read less than 12 V. 

 

 

What is the current in the circuit? 

Page 28: CHAPTER 25 CURRENT, RESISTANCE AND ELECTROMOTIVE FORCEpeople.physics.tamu.edu/adair/phys208/chapt25/CHAPTER 25.pdf · 5 Consider that there are n moving charged particles per volume

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What will the voltmeter read?