1. Current and Resistance
Chapter 22
Current and Resistance
Topics:
Current
Conservation of current
Batteries
Resistance and resistivity
Simple circuits
Sample question:
How can the measurement of an electric current passed through a person’s body allow a determination of the percentage body fat?
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2. Batteries
The potential difference between the terminals of a battery, often called the terminal voltage, is the battery’s emf.
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3. ∆Vchem _____ R I = Simple Circuits
The current is determined by the potential difference and the resistance of the wire:
∆Vchem R
_____
I =
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4. What do we know about batteries and current?
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Copyright © 2007, Pearson Education, Inc., Publishing as Pearson Addison-Wesley.

5. Series and Parallel Series Parallel
Circuit elements in a chain between 2 points
Same current flows through circuit elements I1 = I2
Electric Potentials add => Delta Vtotal = Delta V1 + Delta V2
Parallel
Circuit elements on multiple paths connecting the same points
Since paths connect the same points, Delta V’s are the same
Currents Add => Itotal = I1 + I2
Answer:
i) B, C
ii) A, D
iii) E
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6. Checking Understanding
Rank the bulbs in the following circuit according to their brightness, from brightest to dimmest.
A > B > C > D
A = B > C = D
A = D > B = C
B = C > A = D
Answer: C
Bulbs: A&D, B&C
Currents: C
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7. Answer
Rank the bulbs in the following circuit according to their brightness, from brightest to dimmest.
A > B > C > D
A = B > C = D
A = D > B = C
B = C > A = D
Answer: C
Bulbs: A&D, B&C
Currents: C
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8. Conservation of Current
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9. Conservation of Current
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10. The current in the fourth wire is
QuickCheck 30.6
The current in the fourth wire is
16 A to the right.
4 A to the left.
2 A to the right.
2 A to the left.
Not enough information to tell.
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11. The current in the fourth wire is
QuickCheck 30.6
The current in the fourth wire is
16 A to the right.
4 A to the left.
2 A to the right.
2 A to the left.
Not enough information to tell.
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12. Checking Understanding
The wires below carry currents as noted. Rate the currents IA, IB and IC:
Answer: C
Bulbs: A&D, B&C
Currents: C
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13. Answer
The wires below carry currents as noted. Rate the currents IA, IB and IC:
Answer: C
Bulbs: A&D, B&C
Currents: C
Slide 22-19

14. Batteries and emf
A capacitor quickly runs out of excess charge, but a wire connecting the battery terminals can keep the charges in motion.

15. Batteries and emf
The inner workings of a battery act like a charge escalator between the two terminals.
Charges are removed from the negative terminal and “lifted” to the positive terminal.

16. Batteries and emf
The charge escalator in a battery sustains the current in a wire by providing a continuously renewed supply of charges at the positive terminal.
Once a charge reaches the positive terminal, it can flow downhill through the wire until it reaches the negative terminal again.
The flow of charge in a continuous loop is called a complete circuit.

17. Batteries and emf
The charge escalator in a battery is powered by chemical reactions. Chemicals called electrolytes are sandwiched between two electrodes of different material. The chemicals react and move the positive ions to one electrode, the negative ions to the other.
A dead battery is one in which the supply of chemicals has been exhausted.

18. Batteries and emf
By separating charge, a charge escalator establishes the potential difference between the terminals of a battery.
The potential difference established by a device, such as a battery, that can actively separate charge is called emf.
The symbol for emf is and its units are volts.
A capacitor stores separated charges, but has no means to do the separation. A charged capacitor has a potential difference but not an emf.

19. Batteries and emf
The rating of a battery, such as 1.5 V, is the battery’s emf. It is determined by the chemicals in the battery.
A battery with no current in it has a potential difference equal to its emf. With a current, the battery’s potential difference is slightly less than its emf. We’ll overlook this small difference and assume ΔVbat = .

20. Batteries and Current
A battery is a source of potential difference ΔVbat.
The battery creates a potential difference between the ends of the wire.
The potential difference in the wire creates an electric field in the wire.
The electric field pushes a current I through the wire.
The current in the wire is:
I = ΔVwire/R
Graph V for circuit
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21. QuickCheck 30.11
The current through a wire is measured as the potential difference ΔV is varied. What is the wire’s resistance?
0.01 Ω.
0.02 Ω.
50 Ω.
100 Ω.
Some other value.
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22. QuickCheck 30.11
The current through a wire is measured as the potential difference ΔV is varied. What is the wire’s resistance?
0.01 Ω.
0.02 Ω.
50 Ω.
100 Ω.
Some other value.
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23. Diodes, batteries, and capacitors are all nonohmic devices.
Nonohmic Materials
Some materials and devices are nonohmic, meaning that the current through the device is not directly proportional to the potential difference.
Diodes, batteries, and capacitors are all nonohmic devices.
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24. Electrical Measurements of Physical Properties
Different tissues in the body have different resistivities. Fat has a higher resistivity than muscle, and so a higher resistance in the body indicates a higher proportion of fat.
Electrical impedance tomography passes a small current through a patient’s torso to measure the resistance of intervening tissue.

25. Electrical Measurements of Physical Properties
An image of a patient’s torso generated from the resistance between many pairs of electrodes shows decreasing resistance in red, and increasing resistance in blue.
Blood is a better conductor than tissues of the heart and lungs, so the motion of blood decreased the patient’s resistance of the heart and increased that of the lungs.
In a patient with circulatory problems, any deviation from normal blood flow would lead to abnormal patterns of resistance in this image.

26. Ohm’s Law and Resistor Circuits
Ohm’s Law describes the relationship between the potential difference across a conductor and the current passing through it:
If a graph of I vs. Delta V is linear, we say that the device is ohmic

27. Ohm’s Law and Resistor Circuits
The current through an ohmic material is directly proportional to the potential difference.
Other material and devices are nonohmic, meaning the current through the device is not directly proportional to the potential difference.
Nonohomic devices include batteries and capacitors.

28. Resistivity
Resistivity ρ characterizes the electrical properties of materials.
Materials that are good conductors have low resistivity. Materials that are poor conductors (and thus good insulators) have high resistivity.
The resistivity of a metal decreases with increasing temperature.

29. Resistivity

30. Resistivity
The resistance of a wire depends on its dimensions and the resistivity of its material:
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31. QuickCheck 30.10
Wire 2 is twice the length and twice the diameter of wire 1. What is the ratio R2/R1 of their resistances?
1/4.
1/2. 1. 2. 4.
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32. QuickCheck 30.10
Wire 2 is twice the length and twice the diameter of wire 1. What is the ratio R2/R1 of their resistances?
1/4.
1/2. 1. 2. 4.
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33. Checking Understanding
A battery is connected to a wire, and makes a current in the wire.
Which of the following changes would increase the current?
Which would decrease the current?
Which would cause no change?
Increasing the length of the wire
Keeping the wire the same length, but making it thicker
Using a battery with a higher rated voltage
Making the wire into a coil, but keeping its dimensions the same
Increasing the temperature of the wire
Answer:
i) B, C
ii) A, D
iii) E
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34. Example Problem
The filament of a 100-W bulb carries a current of 0.83 A at the normal operating voltage of 120 V.
What is the resistance of the filament?
If the filament is made of tungsten wire of diameter mm, how long is the filament?
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35. Conceptual Example Problem
If you use wire of the same diameter operating at the same temperature, should you increase or decrease the length of the wire from the value calculated in the previous example in order to make a 60 W light bulb? (Hint: The bulb is dimmer. What does this tell us about the current?)
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36. Short Circuits and Open Circuits – Circuit WS 1
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37. Power in Circuits
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38. Energy and Power in Resistors
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39. Checking Understanding
A resistor is connected to a 3.0 V battery; the power dissipated in the resistor is 1.0 W. The battery is traded for a 6.0 V battery. The power dissipated by the resistor is now
1.0 W
2.0 W
3.0 W
4.0 W
Answer: D
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40. Answer
A resistor is connected to a 3.0 V battery; the power dissipated in the resistor is 1.0 W. The battery is traded for a 6.0 V battery. The power dissipated by the resistor is now
1.0 W
2.0 W
3.0 W
4.0 W
Answer: D
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41. Example Problem
An electric blanket has a wire that runs through the interior.
A current causes energy to be dissipated in the wire, warming the blanket. A new, low-voltage electric blanket is rated to be used at 18 V.
It dissipates a power of 82 W.
What is the resistance of the wire that runs through the blanket?
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42. Conceptual Example Problem: Electric Blankets
For the electric blanket of the previous example, as the temperature of the wire increases, what happens to the resistance of the wire? How does this affect the current in the wire? The dissipated power?
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43. Conductivity and Resistivity
This woman is measuring her percentage body fat by gripping a device that sends a small electric current through her body. Because muscle and fat have different resistivities, the amount of current allows the fat-to-muscle ratio to be determined.
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44. Example Problem: Measuring Body Fat
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45. Analyzing a Simple Circuit
In a circuit using a battery, a lightbulb, and wires (a flashlight), the lightbulb has a resistance of ~3 Ω. The wires typically have a much lower resistance.
We use an ideal wire where its resistance is 0. The potential difference in the wire is 0, even if there is current in it.

46. Analyzing a Simple Circuit
For the ideal-wire model, two wires are connected to a resistor. Current flows through all three, but the current only requires a potential difference across the resistor.

47. Analyzing a Simple Circuit
Current moves in the direction of decreasing potential, so there is a voltage drop when the current passes through the resistor left to right.

48. Analyzing a Simple Circuit
The electric field in a resistor carrying a current in a circuit is uniform. The strength of the electric field is

49. Summary: General Principles
Text: p. 720

50. Summary: Important Concepts

51. Summary: Important Concepts

52. Summary: Applications

53. Summary: Applications

54. Summary

55. Summary

56. Summary