Resistance Is Futile Physics 2102 Jonathan Dowling Physics 2102 Lecture 10 TUE 23 FEB Current Resistance I Georg Simon Ohm 1789 1854 EXAM I AVERAGE 55 100 STANDARD DEVIATION 15 100 APPROXIMATE EXAM I LETTER GRADE A 100 80 B 79 70 C 69 40 D 39 30 F 29 0 We do not assign an official letter grade for any midterm exam so the above breakdown is an unofficial guide for use by students in our section only to give you an APPROXIMATE idea of where you stand The Exam I solutions have been posted at http www phys lsu edu classes spring2010 phys2102 exam1solutions pdf Exam I Problem 2 Integration with Cylindrical Shells dr Qenc r dV V Qenc V unless is a contant ar2 is NOT a constant dV L V r2L dV 2 rdrL r2 a Qtot ar 2 rLdr a r L 2 2 4 2 0 r1 b Qenc ar 2 rLdr a r L 2 mC5 2 0 4 1 m4 m 1 1 C m4 m m5 1 1 Resistance is NOT Futile Electrons are not completely free to move in a conductor They move erratically colliding with the nuclei all the time this is what we call resistance The resistance is related to the potential we need to apply to a device to drive a given current through it The larger the resistance the larger the potential we need to drive the same current Ohm s laws R V i Units R and therefore i V R and V iR Volt Ohm abbr Ampere Georg Simon Ohm 1789 1854 a professor who preaches such heresies is unworthy to teach science Prussian minister of education 1830 Devices specifically designed to have a constant value of R are called resistors and symbolized by dq C Ampere A i s dt Current Density and Drift Speed Vector Same direction as E J such that i J dA The current is the flux of the current density If surface is perpendicular to a constant electric field then i JA or J i A Units J J Ampere m2 dA E i Drift speed vd Velocity at which electrons move in order to establish a current Charge q in the length L of conductor q n A L e L n density of electrons e electric charge A E i L t vd q n ALe i n A e vd L t vd i J n Ae n e J n e vd vd Resistivity and resistance Metal field lines These two devices could have the same resistance R when measured on the outgoing metal leads However it is obvious that inside of them different things go on resistivity E or as vectors E J J Resistivity is associated resistance R V I m Ohm meter with a material resistance with respect to a device 1 Conductivi ty constructed with the material Example A L V V E L i J A Makes sense For a given material V L RA i L A R L A Longer More resistance Thicker Less resistance Resistivity and Temperature Resistivity depends on temperature 0 1 T T0 At what temperature would the resistance of a copper conductor be double its resistance at 20 0 C Does this same doubling temperature hold for all copper conductors regardless of shape or size b a Power in electrical circuits A battery pumps charges through the resistor or any device by producing a potential difference V between points a and b How much work does the battery do to move a small amount of charge dq from b to a dW dU dq V dq dt dt V iV dt The battery power is the work it does per unit time P dW dt iV P iV is true for the battery pumping charges through any device If the device follows Ohm s law i e it is a resistor then V iR and P iV i2R V2 R Ohm s Law and Power in Resistors Watt You Looking At Ohm s Law V Units R Ohm A V iR Power Dissipated by a Resistor P iV i R V R 2 2 s W Watt Units P J L A r2 A Current Density J i A Units A m2 Resistance R L A Resitivity depends only on Material and Temperature Units m Example A human being can be electrocuted if a current as small as i 100 mA passes near the heart An electrician working with sweaty hands makes good contact with the two conductors he is holding If his resistance is R 1500 what might the fatal voltage be Ans 150 V Use V iR Example Two conductors are made of the same material and have the same length Conductor A is a solid wire of diameter r 1 0mm Conductor B is a hollow tube of outside diameter 2r 2 0mm and inside diameter r 1 0mm What is the resistance ratio RA RB measured between their ends A R L A B AA r2 AB 2r 2 r2 3 r2 RA RB AB AA 3 LA LB L Cancels Integration with Cylindrical Shells dr ienc J dA J dA cos A A ienc J A unless J is constant J r ar2 is NOT a constant i L A r2 dA 2 rdr dA r2 itot ar 2 rdr a r 2 2 4 2 0 r1 ienc ar 2 rdr a r 2 Cm 4s 2 0 4 1 m4 1 C s m4 m4 1 Example A P 1250Watt radiant heater is constructed to operate at V 115Volts a What will be the current in the heater b What is the resistance of the heating coil c How much thermal energy is produced in 1 0 hr by the heater Formulas P i2R V2 R V iR Know P V need R to calculate current P 1250W V 115V R V2 P 115V 2 1250W 10 6 i V R 115V 10 6 10 8 A Energy P dU dt U P t 1250W 3600 sec 4 5 MJ 1 250kW hr Example A 100 W lightbulb is plugged into a standard 120 V outlet a What is the resistance of the bulb b What is the current in the bulb c How much does it cost per month to leave the light turned on continuously Assume electric energy costs 6 kW h d Is the resistance different when the bulb is turned off Resistance same as before R V2 P 144 Current same as before i V R 0 83 A We pay for energy used kW h U Pt 0 1kW 30 24 h 72 kW h 4 32 d Resistance should be the same but it s not resistivity and resistance increase with temperature When the bulb is turned off it is colder than when it is turned on so the resistance is lower Example An electrical cable consists of 105 strands of fine wire each having 2 35 resistance The same potential difference is applied between the ends of all the strands and results in a total current of 0 720 …
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