PHYS 1444 – Section 004Lecture #10Temperature Dependence of ResistivityElectric EnergyElectric PowerExample 25 – 7Power in Household CircuitsExample 25 – 10Alternating CurrentAlternating CurrentAlternating CurrentPower Delivered by Alternating CurrentPower Delivered by Alternating CurrentExample 25 – 11PHYS 1444 – Section 004Lecture #10Wednesday, Feb. 21 2007Dr. Andrew BrandtWednesday, Feb. 21, 2007 1PHYS 1444-004, Spring 2007Dr. Andrew Brandt•Resistivity• Electric Power• Alternating Current• Microscopic View of CurrentHW4 due Fri 2/23 at 8 pm;HW5 will be due Fri Mar. 2;Test Ch 21-25 Mon Mar. 5Wednesday, Feb. 21, 2007 2PHYS 1444-004, Spring 2007Dr. Andrew Brandt• Do you think the resistivity depends on temperature?–Yes• Would it increase or decrease with the temperature?–Increase–Why?– Since the atoms are vibrating more rapidly as temperature increases and are arranged in a less orderly fashion. So?• They might interfere more with the flow of electrons.• If the temperature change is not too large, the resistivity of metals usually increase nearly linearly w/ temperature– α is the temperature coefficient of resistivity– α of some semiconductors can be negative due to the increased number of free electrons.()001TTTρρ α⎡⎤=+−⎣⎦Temperature Dependence of ResistivityElectric Energy• Why is electric energy useful?– It can be transform easily into different forms of energy:• Motors, pumps, etc, transform electric energy to mechanical energy • Heaters, dryers, cook-tops, etc., transform electricity to thermal energy• Light bulb filaments transform electric energy to light energy– Only about 10% of the energy turns to light with 90% lost via heat– Typical household light bulb and heating elements have resistance of order few ohms to few hundred of ohms• How does electric energy transform to thermal energy?– Flowing electrons collide with the vibrating atoms of the wire.– In each collision, part of electron’s kinetic energy is transferred to the atom it collides with.– The kinetic energy of wire’s atoms increases, and thus the temperature of the wire increases.– The increased thermal energy can be transferred as heat through conduction and convection to the air in a heater or to food in a pan; it can also be radiated as light.Wednesday, Feb. 21, 2007 3PHYS 1444-004, Spring 2007Dr. Andrew BrandtWednesday, Feb. 21, 2007 4PHYS 1444-004, Spring 2007Dr. Andrew BrandtElectric Power• How do we find out the power of an electric device?– What is definition of the power?• The rate at which work is done or the energy is transferred• What energy is transferred when an infinitesimal charge dqmoves through a potential difference V?–dU=Vdq– If dt is the time required for an amount of charge dq to move through the potential difference V, the power P is –– Thus, we obtain . – What is the unit?– What kind of quantity is the electrical power? •Scalar– P=IV can apply to any devices while the formulae involving resistance only apply to Ohmic resistors.P=What is this?dU dt =Vdq dtPVI=Watts = J/s 22VPIRR==In terms of resistanceExample 25 – 7 Headlights: Calculate the resistance of a 40-W automobile headlight designed for a 12V battery. Since the power is 40W and the voltage is 12V, we use the formula with V and R. 2VPR=Solve for RR=2VP=()2123.640VW=ΩWednesday, Feb. 21, 2007 5PHYS 1444-004, Spring 2007Dr. Andrew BrandtWednesday, Feb. 21, 2007 6PHYS 1444-004, Spring 2007Dr. Andrew BrandtPower in Household Circuits• Household devices usually have small resistance– But since they draw current, if they become large enough, wires can heat up (overload) and cause a fire• Why is using thicker wires safer?– Thicker wires has less resistance, lower heat• How do we prevent this?– Put in a switch that disconnects the circuit when overloaded• Fuse or circuit breakers• They open up the circuit when the current exceeds a certain valueOverloadWednesday, Feb. 21, 2007 7PHYS 1444-004, Spring 2007Dr. Andrew BrandtExample 25 – 10 Will a fuse blow?: Determine the total current drawn by all the devices in the circuit in the figure.The total current is the sum of current drawn by the individual devices. Solve for IPIV=Bulb IPV=BI=Heater HI=Stereo SI =Dryer DI=Total current TI =BHSDIIII+++=0.8 15.0 2.9 10.0 28.7AAA A A+++ =1200 120 10.0WV A=1800 120 15.0WV A=135 120 2.9WV A=100 120 0.8WV A=What is the total power? TP=BHSDPPPP+++=100 1800 350 1200 3450WWWWW+++ =Wednesday, Feb. 21, 2007 8PHYS 1444-004, Spring 2007Dr. Andrew BrandtAlternating Current• Does the direction of the flow of current change when a battery is connected to a circuit?–No. Why?• Because its source of potential difference is constant.– This kind of current is called the Direct Current (DC), and it does not change its direction of flow.• How would DC look as a function of time?– A straight line• Electric generators at electric power plant produce alternating current (AC)– AC reverses direction many times a second– AC is sinusoidal as a function of time• Most currents supplied to homes and business are AC.Alternating Current• The voltage produced by an AC electric generator is sinusoidal– This is why the current is sinusoidal• Voltage produced can be written as • What are the maximum and minimum voltages?–V0and –V0– The potential oscillates between +V0and –V0, the peak voltages or amplitude– What is f ?• The frequency, the number of complete oscillations made per second. What is the unit of f ? What is the normal size of f in the US?–f = 60 Hz in the US and Canada. – Many European countries have f = 50Hz.– ω=2πfV =0sin 2Vftπ=0sinVtωWednesday, Feb. 21, 2007 9PHYS 1444-004, Spring 2007Dr. Andrew BrandtAlternating Current• Since V=IR, if a voltage V exists across a resistance R, the current I is• What are the maximum and minimum currents?–I0and –I0– The current oscillates between +I0and –I0, the peak currents or amplitude. The current is positive when electron flows in one direction and negative when they flow in the opposite direction.– What is the average current?• Zero. So there is no power and no heat is produced in a heater?– Yes there is! The electrons actually flow back and forth, so power is delivered.VIR==0sin 2VftRπ=0sinItωWhat is this?Wednesday, Feb. 21, 2007 10PHYS 1444-004, Spring 2007Dr. Andrew BrandtPower Delivered by Alternating
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