Physics Physics 122B 122B Electricity Electricity and and Magnetism Magnetism Lecture 15 (Knight: 31.5 to 31.8) Resistors in Circuits April 30, 2007 Martin Savage 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 02/08/20
Physics 122B - Lecture 15 2 material inclusive. Units of Power Power units watts W VA J/s Energy units 1 kilowatt-hour (1.0 103 W)(3600 s) 3.6 106 J 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. 02/08/20 Physics 122B - Lecture 15 3 Question Which resistor dissipates the most power? 02/08/20
Physics 122B - Lecture 15 4 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. 02/08/20 Physics 122B - Lecture 15 5 Resistors in Series
Vab V1 V2 IR1 IR2 I ( R1 R2 ) Vab I ( R1 R2 ) Rab R1 R2 I I Req R1 R2 RN (series resistors) 02/08/20 Physics 122B - Lecture 15 6 Example: Example: A A Series Series Resistor Resistor Circuit Circuit Req 15 4 8 27 E
(9 V) I 0.333 A Req (27 ) VR1 IR1 (15 )(0.333 A) 5.0 V VR2 IR2 (4 )(0.333 A) 1.33 V VR3 IR3 (8 )(0.333 A) 2.67 V 02/08/20 Physics 122B - Lecture 15 7 Ammeters x x I=? Answer: You must break Question: How do you the circuit and insert an measure the current in a
ammeter into the line of circuit? Ideal Ammeter: To have a minimum current flow. 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 02/08/20 Physics 122B - Lecture 15 8 induction (see L20). 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 02/08/20 Physics 122B ideal - Lecture 15 battery. 9 Real Batteries (2) Vbat E I rint E I E E Req R rint VR IR
Vbat R E R rint Vbat E I rint E rint E R rint rint R =E 1 E = R rint R rint 02/08/20 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 E. Then
R=rint because each drops E. Physics 122B - Lecture 15 10 Example: Example: Lighting Lighting Up Up a a Flashlight Flashlight A 6 flashlight bulb is powered by a 3 V battery having an internal resistance of 1 . (Assume ideal wires.) 1/ What is the power dissipation of the bulb? 2/ What is the terminal voltage of the battery? E (3 V) I 0.43 A R r (6 ) (1 ) PR I 2 R (0.43 A) 2 (6 ) 1.1 W Vbat E I r (3 V) (0.43 A)(1 ) 2.57 V Note that in this situation, 14% of the available energy goes
into heating the battery rather than providing light from the bulb. 02/08/20 Physics 122B - Lecture 15 11 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 batterys 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). 02/08/20
Physics 122B - Lecture 15 12 Example: Example: A A Short-Circuited Short-Circuited Car Battery Battery What is the short-circuit current of a 12 V car battery with an internal resistance of 0.020 ? What happens to the power supplied by the battery when it is shorted? I short E (12 V) 600 A r (0.020 ) P I 2 r (600 A) 2 (0.020 ) 7, 200 W
0.02 12 V All of this power would be dissipated internally in the battery, making it likely to explode. Therefore, do not short out your cars battery! 02/08/20 Physics 122B - Lecture 15 13 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? 1. Bulb A gets brighter (because the overall current increases); 2. Bulb B gets dimmer (because current is diverted to Bulb C);
3. Bulb C glows with the same brightness as B (because they split the current equally). 02/08/20 Physics 122B - Lecture 15 14 Resistors in Parallel I I1 I 2 V1 V2 R1 R2 1 1 Vcd Vcd Vcd R1 R2 R1 R2
(parallel resistors) Physics 122B - Lecture 15 15 Series vs. Parallel V R1 R2 Resistors in series divide the overall potential difference between them in proportion to their R1 resistances. I 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. 02/08/20 Physics 122B - Lecture 15 16 Example: Example: A A Parallel Parallel Resistor Resistor Circuit 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
4 8 I1 I1 I2 I E (9 V) 3.98 A Req (2.26 ) V2 (9.0 V) 2.25 A R2
(4 ) Physics 122B - Lecture 15 I3 V3 (9.0 V) 1.13 A R3 (8 ) 17 Example: Example: A A Combination Combination of of Resistors Resistors 02/08/20 Physics 122B - Lecture 15 18
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. 02/08/20 Physics 122B - Lecture 15 19 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. 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. 02/08/20 Physics 122B - Lecture 15 V A I X I 20 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> 02/08/20 Physics 122B - Lecture 15 21 Example: Example: Analyzing Analyzing a Complex Circuit (1) (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.
02/08/20 Physics 122B - Lecture 15 22 Example: Example: Analyzing Analyzing a Complex Circuit (2) (2) 02/08/20 Physics 122B - Lecture 15 23 End of Lecture 15 Before the next lecture, read Knight, sections 31.9 through 31.10. Lecture HW Assignment #5 has been posted on the Tycho system and is due at 10 PM Wednesday.
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