PHYS 1444 – Section 02 Lecture #10Ohm’s Law: ResistorsOhm’s Law: Resistor ValuesResistivityExample 25 – 4Example 25 – 5Temperature Dependence of ResistivityElectric EnergyElectric PowerExample 25 – 7Power in Household CircuitsExample 25 – 10Alternating CurrentSlide 14Slide 15Thursday, Feb. 24, 2011 1PHYS 1444-02 Dr. Andrew BrandtPHYS 1444 – Section 02Lecture #10•Chapter 25 Thursday Feb 24, 2011Dr. Andrew BrandtHW4 Ch 24 due Sat Feb. 26thMar 3 will be ½ period reviewHW5 Ch 25 will be due Fri. Mar. 4March 4: deadline to receive credit for late HW so solutions can be posted***Test 1 will be Tues. Mar. 8 on ch 21-25***•Ohm’s Law: Resistors•Resistivity•Electric Power•Alternating CurrentThursday, Feb. 24, 2011 2PHYS 1444-02 Dr. Andrew BrandtOhm’s Law: Resistors•All electric devices offer resistance to the flow of current.–Filaments of light bulbs or heaters are wires with high resistance causing electrons to lose their energy in the wire–In general connecting wires have low resistance compared to other devices in the circuit•In circuits, resistors are used to control the amount of current–Resistors offer resistance of less than one ohm to millions of ohms–Main types are•“wire-wound” resistors which consists of a coil of fine wire•“composition” resistors which are usually made of semiconductor carbon•thin metal films•When drawn in the circuit, the symbol for a resistor is:•Wires are drawn simply as straight linesThursday, Feb. 24, 2011 3Ohm’s Law: Resistor Values•Resistors have their resistance color-coded on its body•The color-coding follows the convention below: Color Number Multiplier ToleranceBlack 0 1=100Brown 1 101Red 2 102Orange 3 103Yellow 4 104Green 5 105Blue 6 106Violet 7 107Gray 8 108White 9 109Gold 10-15%Silver 10-210%None 20%What is the resistance of the resistor in this figure?25310�10%�PHYS 1444-02 Dr. Andrew BrandtThursday, Feb. 24, 2011 4PHYS 1444-02 Dr. Andrew BrandtResistivity•It is experimentally found that the resistance R of a metal wire is directly proportional to its length l and inversely proportional to its cross-sectional area A–How would you formularize this?–The proportionality constant is called the resistivity and depends on the material used. What is the unit of this constant?•ohm-m or m•The values depends on material, purity, temperature, etc–How would you interpret the resistivity?•The higher the resistivity the higher the resistance•The lower the resistivity the lower the resistance and the higher the conductivity Silver has the lowest resistivity.–So silver is the best conductor–The reciprocal of the resistivity is called the conductivity, ,lRAr=1sr=AlThursday, Feb. 24, 2011 5PHYS 1444-02 Dr. Andrew BrandtExample 25 – 4 Speaker wires: Suppose you want to connect your stereo to remote speakers. (a) If each wire must be 20m long, what diameter copper wire should you use to keep the resistance less than 0.1 per wire? (b) If the current on each speaker is 4.0A, what is the voltage drop across each wire?The resistivity of copper is From Ohm’s law, V=IR, we obtainFrom the formula for resistance, we can obtain the area V =81.68 10Cumr-= � W�R =Solve for AA =d =lArlRr =2rp2r =831.68 10 202 2.1 10 2.10.1m mm mmp--� W� �= � =� WSolve for dTable 25.1 2lRrp=IR =4.0 0.1 0.4A V� W=Thursday, Feb. 24, 2011 6PHYS 1444-02 Dr. Andrew BrandtExample 25 – 5 Stretching changes resistance: A wire of resistance R is stretched uniformly until it is twice its original length. What happens to its resistance?What is the constant quantity in this problem? What is the volume of a cylinder of length L and radius r? R =lArV =The volume! What happens to A if L increases factor two, L’=2L? The cross-sectional area, A, halves. A’=A/2The original resistance is The new resistance is 'R =''LAr =22LAr =4LAr =4RThe resistance of the wire increases by a factor four if the length is doubled (fixed V). AL =2r LpThursday, Feb. 24, 2011 7PHYS 1444-02 Dr. Andrew Brandt•Do you think the resistivity depends on temperature?–Yes (or at least you should!)•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– is the temperature coefficient of resistivity– of some semiconductors can be negative due to the increased number of free electrons.( )0 01TT Tr r a� �= + -� � Temperature Dependence of ResistivityThursday, Feb. 24, 2011 8PHYS 1444-02 Dr. Andrew BrandtElectric 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.Thursday, Feb. 24, 2011 9PHYS 1444-02 Dr. 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 dq moves 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 applies to Ohmic resistors.P =What is
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