Physics 2102 Spring 2007 Lecture 10 Current and Resistance

Transcription

1 esstance Is Futle! Physcs 0 Sprng 007 Jonathan Dowlng Physcs 0 Sprng 007 Lecture 0 Current and esstance Georg Smon Ohm ( )

2 What are we gong to learn? A road map lectrc charge lectrc force on other electrc charges lectrc feld, and electrc potental Movng electrc charges : current lectronc crcut components: batteres, resstors, capactors lectrc currents Magnetc feld Magnetc force on movng charges Tme-varyng magnetc feld lectrc Feld More crcut components: nductors. lectromagnetc waves lght waves Geometrcal Optcs (lght rays). Physcal optcs (lght waves)

3 The resstance s related to the potental we need to apply to a devce to drve a gven current through t. The larger the resstance, the larger the potental we need to drve the same current. V! and therefore : Ohm s laws V and V Volt Unts :[] " Ohm (abbr.!) Ampere esstance lectrons are not completely free to move n a conductor. They move erratcally, colldng wth the nucle all the tme: ths s what we call resstance. Georg Smon Ohm ( ) "a professor who preaches such hereses s unworthy to teach scence. Prussan mnster of educaton 830 Devces specfcally desgned to have a constant value of are called resstors, and symbolzed by

4 Current densty and drft speed Vector : J r Same drecton as r r r such that! J " da The current s the flux of the current densty! If surface s perpendcular to a constant electrc feld, then JA, or J/A J da Unts: [ J ] Ampere m Drft speed: v d :Velocty at whch electrons move n order to establsh a current. L Charge q n the length L of conductor: q ( n AL) e A n densty of electrons, e electrc charge t L v d q n ALe t L v d n Aev d v d n Ae r r J n ev d J n e

5 esstvty and resstance Metal feld lnes These two devces could have the same resstance, when measured on the outgong metal leads. However, t s obvous that nsde of them dfferent thngs go on. r resstvty:! or, as vectors, J ( resstance: V/I ) esstvty s assocated wth a materal, resstance wth respect to a devce Conductv ty : " constructed wth the materal.! r! J xample: - L V A + V, J L A! Makes sense! For a gven materal: V L A A L Longer! Thcker L! A More resstance! Less resstance

6 esstvty and Temperature esstvty depends on temperature: ρ ρ 0 (+α (T-T 0 ) ) At what temperature would the resstance of a copper conductor be double ts resstance at 0.0 C? Does ths same "doublng temperature" hold for all copper conductors, regardless of shape or sze?

7 b a Power n electrcal crcuts A battery pumps charges through the resstor (or any devce), by producng a potental dfference V between ponts 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 V dt The battery power s the work t does per unt tme: PdW/dtV PV s true for the battery pumpng charges through any devce. If the devce follows Ohm s law (.e., t s a resstor), then V and PV V /

8 xample A human beng can be electrocuted f a current as small as 50 ma passes near the heart. An electrcan workng wth sweaty hands makes good contact wth the two conductors he s holdng. If hs resstance s 500, what mght the fatal voltage be? (Ans: 75 V)

9 xample Two conductors are made of the same materal and have the same length. Conductor A s a sold wre of dameter.0 mm. Conductor B s a hollow tube of outsde dameter.0 mm and nsde dameter.0 mm. What s the resstance rato A / B, measured between ther ends? A ρl/a B A A π r A B π ((r) r )3πr A / B A B /A A 3

10 xample A 50 W radant heater s constructed to operate at 5 V. (a) What wll be the current n the heater? (b) What s the resstance of the heatng col? (c) How much thermal energy s produced n.0 h by the heater? Formulas: P V /; V Know P, V; need to calculate current! P50W; V5V > V /P(5V) /50W0.6 Ω V/ 5V/0.6 Ω0.8 A nergy? PdU/dt > dup dt 50W 3600 sec 4.5 MJ

11 xample A 00 W lghtbulb s plugged nto a standard 0 V outlet. (a) (b) (c) (d) What s the resstance of the bulb? What s the current n the bulb? How much does t cost per month to leave the lght turned on contnuously? Assume electrc energy costs 6 /kw h. Is the resstance dfferent when the bulb s turned off? esstance: same as before, V /P44 Ω Current, same as before, V/0.83 A We pay for energy used (kw h): UPt0.kW (30 4) h 7 kw h > $4.3 (d): esstance should be the same, but t s not: resstvty and resstance ncrease wth temperature. When the bulb s turned off, t s colder than when t s turned on, so the resstance s lower.

12 xample An electrcal cable conssts of 05 strands of fne wre, each havng.35 Ω resstance. The same potental dfference s appled between the ends of all the strands and results n a total current of 0.70 A. (a) What s the current n each strand? [ ] A (b) What s the appled potental dfference? [.6e-08] V (c) What s the resstance of the cable? [.4e-08 ]

13 MF devces and sngle loop crcuts b The battery operates as a pump that moves postve charges from lower to hgher electrc potental. A battery s an example of an electromotve force (MF) devce. a These come n varous knds, and all transform one source of energy nto electrcal energy. A battery uses chemcal energy, a generator mechancal energy, a solar cell energy from lght, etc. The dfference n potental energy that the devce establshes s called the MF and denoted by Ε. a + b c d V a +Ε V a Ε Ε V a a b c da

14 Crcut problems b a Gven the emf devces and resstors n a crcut, we want to calculate the crculatng currents. Crcut solvng conssts n takng a walk along the wres. As one walks through the crcut (n any drecton) one needs to follow two rules: When walkng through an MF, add +Ε f you flow wth the current or Ε otherwse. How to remember: current gans potental n a battery. When walkng through a resstor, add -, f flowng wth the current or + otherwse. How to remember: resstors are passve, current flows potental down. xample: Walkng clockwse from a: +Ε-0. Walkng counter-clockwse from a: Ε+0.

15 Ideal batteres vs. real batteres If one connects resstors of lower and lower value of to get hgher and hgher currents, eventually a real battery fals to establsh the potental dfference Ε, and settles for a lower value. One can represent a real MF devce as an deal one attached to a resstor, called nternal resstance of the MF devce: true true r nt true! r nt The true MF s a functon of current.

16 esstors n Seres +!! tot 0 +! ( + ) tot Behave lke capactors n parallel! If you have n resstors n seres : tot! n

17 esstors n parallel + a 3 Node a : + Left loop :! 3 Outer loop : !! 3 + & $ % + #! " + a tot tot & $ % + #! " Same as capactors n seres. For n resstors : tot & $ % n ' #! "

18 xample Bottom loop: (all else s rrelevant) V 8Ω V V. A 8! 5