1. Physics 122B Electricity and Magnetism
Lecture 15 (Knight: 31.5 to 31.8)
Resistors in Circuits
April 30, 2007
Martin Savage

2. Lecture 15 Announcements
Lecture HW Assignment #5 has been posted on the Tycho system and is due at 10 PM on Wednesday.
The second midterm exam is this Friday. It will cover everything up to the end of Wednesdays lecture, emphasizing the most recent material, but assumes understanding of all material inclusive.
11/11/2018
Physics 122B - Lecture 15

3. Units of Power
At residential rates, Seattle City Light charges about 7.5¢ for a kilowatt hour of electrical energy, so one million joules ( 1 MJ) of electrical energy costs about 2¢. (Remarkably cheap!)
If you operate a 1500 W hair dryer for 10 minutes, you use 0.25 kilowatt hours or 0.9x106 J of energy, which adds about 1.8¢ to your electric bill.
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Physics 122B - Lecture 15

4. Question Which resistor dissipates the most power? 11/11/2018
Physics 122B - Lecture 15

5. Bulbs in Series
Question: How does the brightness of bulb A compare with that of bulbs B and C?
Answer: Bulb A is brighter than bulb B and bulb C, which are of equal brightness.
Reason: The potential drop across bulb A is E, while the potential drop across B and across C is E/2.
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Physics 122B - Lecture 15

6. Resistors in Series
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7. Example: A Series Resistor Circuit
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Physics 122B - Lecture 15

8. Ammeters x x Question: How do you measure the current in a circuit?
Answer: You must break the circuit and insert an ammeter into the line of current flow.
Ideal Ammeter: To have a minimum effect on the circuit being measured, the inserted ammeter must have zero resistance, so that there is zero potential difference across the ammeter. Electronic ammeters can give good approximations to this condition, but electro-mechanical ammeters may not.
Note: “Clip on” ammeters that measure AC current without breaking the circuit are commercially available. They use magnetic induction (see L20).
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Physics 122B - Lecture 15

9. Real Batteries (1)
An ideal battery provides a potential difference that is a constant, independent of current flow or duration of use.
But real batteries “sag” under load and become “weak” or “dead” as their chemical energy is used up. How can we include such effects?
A reasonable approximation is to include an internal resistance rint. The internal resistance may increase as the battery ages and supplies energy. The rule is that the larger and more expensive the battery, the lower is rint.
A regulated electronic power supply provides a very good approximation to a zero-resistance constant-potential ideal battery.
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Physics 122B - Lecture 15

10. Real Batteries (2) DVbat Question: How can you measure rint?
Answer: One (rather brutal) way is to vary an external load resistance R until the potential drop across R is ½E. Then R=rint because each drops ½E.
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Physics 122B - Lecture 15

11. Example: Lighting Up a Flashlight
A 6 W flashlight bulb is powered by a 3 V battery having an internal resistance of 1 W. (Assume ideal wires.)
What is the power dissipation of the bulb?
What is the terminal voltage of the battery? 1/ 2/
Note that in this situation, 14% of the available energy goes into heating the battery rather than providing light from the bulb.
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Physics 122B - Lecture 15

12. A Short Circuit
What happens if you “short out” a battery, i.e., connect an ideal resistanceless wire across its terminals, so that the potential difference across the terminals becomes zero?
Then, Ishort=E /r. In other words, all of the battery’s potential is dropped across its internal resistance. Ishort is the maximum possible current that a battery can supply, and is a measure of the internal resistance r of the battery (r = E / Ishort).
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Physics 122B - Lecture 15

13. Example: A Short-Circuited Car Battery
What is the short-circuit current of a 12 V car battery with an internal resistance of W?
What happens to the power supplied by the battery when it is shorted?
0.02 W
12 V
All of this power would be dissipated internally in the battery, making it likely to explode. Therefore, do not short out your car’s battery!
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Physics 122B - Lecture 15

14. Bulbs in Parallel
Initially, bulbs A and B have the same brightness and C is out. What happens to the brightness of the bulbs when the switch is closed?
Bulb A gets brighter (because the overall current increases);
Bulb B gets dimmer (because current is diverted to Bulb C);
Bulb C glows with the same brightness as B (because they split the current equally).
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Physics 122B - Lecture 15

15. Resistors in Parallel
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Physics 122B - Lecture 15

16. Series vs. Parallel DV R1 R2
Resistors in series divide the overall potential difference between them in proportion to their resistances. R1 R2 I
Resistors in parallel divide the overall current through them in proportion to their inverse resistances. The current splits and tends to favor “the path of least resistance”.
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Physics 122B - Lecture 15

17. Example: A Parallel Resistor Circuit
Three resistors are connected across a 9 V battery.
Find the current through the battery.
Find the potential differences across and currents through each resistor. I I1 I2 I3
DVbat
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Physics 122B - Lecture 15

18. Example: A Combination of Resistors
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19. Voltmeters
Question: How do you measure the potential difference between two points in a circuit?
Answer: You can connect one lead of a voltmeter to each point.
Ideal Voltmeter: To have a minimum effect of the circuit being measured, the connected voltmeter must have infinite resistance, so that no current is diverted through the voltmeter. Electronic voltmeters can give good approximations to this condition, but electro-mechanical voltmeters may not.
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Physics 122B - Lecture 15

20. Voltmeters vs. Ammeters
An ideal voltmeter has infinite internal resistance. It must be connected between circuit elements to measure the potential difference between two points in the circuit. V
An ideal ammeter has zero internal resistance. It must be inserted by breaking a circuit connection to measure the current flowing through that connection in the circuit. A I X
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21. Question
What is the correct order of bulb brightness (from brightest to dimmest)?
(The bulbs are identical)
(a) A=B=C=D; (b) A>B=C=D; (c) A=B>C=D; (d) A>B>C=D; (e) A>B>C>D
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Physics 122B - Lecture 15

22. Example: Analyzing a Complex Circuit (1)
Four resistors are connected to a 12 V battery as shown.
Find the current through the battery.
Find the potential differences across and currents through each resistor.
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Physics 122B - Lecture 15

23. Example: Analyzing a Complex Circuit (2)
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24. End of Lecture 15
Before the next lecture, read Knight, sections 31.9 through
Lecture HW Assignment #5 has been posted on the Tycho system and is due at 10 PM Wednesday.
Midterm 2 is Friday
11/11/2018
Physics 122B - Lecture 15