1. General Physics (PHY 2140) Lecture 9 Electrodynamics Electric current
temperature variation of resistance
electrical energy and power
Chapter 17-18
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2. The Physics Resource Center Room 172 of Physics Research Building.
Department of Physics and Astronomy
announces the Fall 2003 opening of
The Physics Resource Center
on Monday, September 22 in
Room 172 of Physics Research Building.
Hours of operation:
Mondays, Tuesdays, Wednesdays AM to 6 PM
Thursdays and Fridays AM to 3 PM
Undergraduate students taking PHY will be able to get assistance in this Center with their homework, labwork and other issues related to their physics course.
The Center will be open: Monday, September 22 to Wednesday, December 10, 2003.
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3. Lightning Review R1 R2 Last lecture: Current and resistance
Current and drift speed
Resistance and Ohm’s law
I is proportional to V
Resistivity
material property
Review Problem: Consider two resistors wired one after another. If there is an electric current moving through the combination, the current in the second resistor is
a. equal to
b. half
c. smaller, but not necessarily half
the current through the first resistor. a b c R1 R2 I
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4. 17.4 Resistivity - Example
(a) Calculate the resistance per unit length of a 22-gauge nichrome wire of radius m.
Cross section:
Resistivity (Table): 1.5 x 10-6 Wm.
Resistance/unit length:
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5. 17.4 Resistivity - Example
(b) If a potential difference of 10.0 V is maintained across a 1.0-m length of the nichrome wire, what is the current?
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6. 17.4 Temperature Variation of Resistance - Intro
The resistivity of a metal depends on many (environmental) factors.
The most important factor is the temperature.
For most metals, the resistivity increases with increasing temperature.
The increased resistivity arises because of larger friction caused by the more violent motion of the atoms of the metal.
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7. r is the resistivity at temperature T (measured in Celsius).
For most metals, resistivity increases approx. linearly with temperature. r T
Metallic Conductor
r is the resistivity at temperature T (measured in Celsius).
ro is the reference resistivity at the reference temperature To (usually taken to be 20 oC).
a is a parameter called temperature coefficient of resistivity.
For a conductor with fixed cross section. r T
Superconductor
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8. 17.5 Temperature Variation of Resistance - Example
Platinum Resistance Thermometer
A resistance thermometer, which measures temperature by measuring the change in the resistance of a conductor, is made of platinum and has a resistance of 50.0 W at 20oC. When the device is immersed in a vessel containing melting indium, its resistance increases to W. Find the melting point of Indium.
Solution:
Using a=3.92x10-3(oC)-1 from table 17.1.
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9. Using a=3.92x10-3(oC)-1 from table 17.1. Ro=50.0 W. To=20oC. R=76.8 W.
Platinum Resistance Thermometer A resistance thermometer, which measures temperature by measuring the change in the resistance of a conductor, is made of platinum and has a resistance of 50.0 W at 20oC. When the device is immersed in a vessel containing melting indium, its resistance increases to W. Find the melting point of Indium.
Solution:
Using a=3.92x10-3(oC)-1 from table 17.1.
Ro=50.0 W.
To=20oC.
R=76.8 W.
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10. Appendix: Superconductivity
1911: H. K. Onnes, who had figured out how to make liquid helium, used it to cool mercury to 4.2 K and looked at its resistance:
At low temperatures the resistance of some metals0, measured to be less than 10-16•ρconductor (i.e., ρ<10-24 Ωm)!
Current can flow, even if E=0.
Current in superconducting rings can flow for years with no decrease!
1957: Bardeen (UIUC!), Cooper, and Schrieffer (“BCS”) publish theoretical explanation, for which they get the Nobel prize in 1972.
It was Bardeen’s second Nobel prize (1956 – transistor)
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11. 17.7 Electrical energy and power
In any circuit, battery is used to induce electrical current
chemical energy of the battery is transformed into kinetic energy of mobile charge carriers (electrical energy gain)
Any device that possesses resistance (resistor) present in the circuit will transform electrical energy into heat
kinetic energy of charge carriers is transformed into heat via collisions with atoms in a conductor (electrical energy loss) I
V = IR + - D C B A
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12. Electrical energy Consider circuit on the right in detail
AB: charge gains electrical energy form the battery
(battery looses chemical energy)
CD: electrical energy lost (transferred into heat)
Back to A: same potential energy (zero) as before
Gained electrical energy = lost electrical energy on the resistor C B A D
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13. Power Compute rate of energy loss (power dissipated on the resistor)
Use Ohm’s law
Units of power: SI: watt
delivered energy: kilowatt-hours
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14. Example Power Transmission line
A high-voltage transmission line with resistance of 0.31 W/km carries 1000A , starting at 700 kV, for a distance of 160 km. What is the power loss due to resistance in the wire?
Given:
V= V
r=0.31 W/km
L=160 km
I=1000 A
Find:
P=?
Observations:
Given resistance/length, compute total resistance
Given resistance and current, compute power loss
Now compute power
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15. Mini-quiz
Why do the old light bulbs usually fail just after you turn them on?
When the light bulb is off, its filament is cold, so its resistance is large. Once the switch it thrown, current passes through the filament heating it up, thus increasing the resistance,
This leads to decreased amount of power delivered to the light bulb, as
Thus, there is a power spike just after the switch is thrown, which burns the light bulb.
Resume: electrical devices are better be turned off if there is a power loss
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16. Direct Current Circuits
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17. 18.1 Sources of EMF
Steady current (constant in magnitude and direction)
requires a complete circuit
path cannot be only resistance
cannot be only potential drops in direction of current flow
Electromotive Force (EMF)
provides increase in potential E
converts some external form of energy into electrical energy
Single emf and a single resistor: emf can be thought of as a “charge pump” I
V = IR E + -
V = IR = E
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18. EMF Each real battery has some internal resistance
AB: potential increases by E on the source of EMF, then decreases by Ir (because of the internal resistance)
Thus, terminal voltage on the battery DV is
Note: E is the same as the terminal voltage when the current is zero (open circuit) B C r R E A D
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19. EMF (continued) Now add a load resistance R
Since it is connected by a conducting wire to the battery → terminal voltage is the same as the potential difference across the load resistance
Thus, the current in the circuit is B C r R E A D
Power output:
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Note: we’ll assume r negligible unless otherwise is stated

20. Measurements
Voltmeters measure Potential Difference (or voltage) across a device by being placed in parallel with the device. V
Ammeters measure current through a device by being placed in series with the device. A
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21. Direct Current Circuits
Two Basic Principles:
Conservation of Charge
Conservation of Energy
Resistance Networks
Req I a b
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22. Conservation of Charge I = I1 = I2 = I3 Conservation of Energy
Resistors in series
Conservation of Charge
I = I1 = I2 = I3
Conservation of Energy
Vab = V1 + V2 + V3 a b I R1
V1=I1R1 R2
V2=I2R2 R3
V3=I3R3
Voltage Divider:
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23. Conservation of Charge I = I1 + I2 + I3 Conservation of Energy
Resistors in parallel
Conservation of Charge
I = I1 + I2 + I3
Conservation of Energy
Vab = V1 = V2 = V3 a R1
V1=I1R1 R2
V2=I2R2 R3
V3=I3R3 b
Current Divider:
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24. R1=4W E=18V R3=6W R2=3W Example:
Determine the equivalent resistance of the circuit as shown.
Determine the voltage across and current through each resistor.
Determine the power dissipated in each resistor
Determine the power delivered by the battery
R1=4W
E=18V
R2=3W
R3=6W
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