lec14_020907_-_Current

lec14_020907_-_Current - Survey 1. The exam covered...

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Unformatted text preview: Survey 1. The exam covered material similar to those on the HW. A. Agree B. Disagree C. Can't tell Can' 2. The exam covered material similar to those in recitation. A. Agree B. Disagree C. Can't tell Can' 3. Did you need to back of the sheets as scratch? A. Yes Friday, 9 February 2007 Big Picture 1. Electrostatics 2. Circuits Capacitors and Dielectrics: Storing Charge Current and Resistance Direct Current Circuits (Steady State and RC) 3. Magnetics 4. Optics 1 Friday, 9 February 2007 2 B. No Current Current is the Rate of Flow of Electric Charge through a cross-sectional area: cross- Question What is the typical drift speed of electrons in a common household wire? A. 108 m/s B. 104 m/s C. 1 m/s D. 10-4 m/s E. 10-8 m/s I= Q t Units: 1 A = 1 C / s (Ampere) Number of charge carriers (electrons) per unit volume: n Charge on each carrier: Wire of cross-sectional area A: cross- q Drift speed of each charge carrier: Distance a charge travels in some time: = v t d vd Total charge that flows through that length, in that time: Q = nqA(vd t ) Current: Friday, 9 February 2007 I= Q = n q Avd t 3 Friday, 9 February 2007 4 1 Drift Speed Let's estimate drift speed: Let' I = (n|q|A)vd (n|q|A)v vd =I / (n|q|A) (n|q|A) Household wire (12 gauge): A = 3.309 mm2 = 3.309 e-6 m2 eCopper: n = na = NA / M = (8.93 g/cm3) (6.02 e23 atoms/mol) / (63.5 g/mol) = 8.47 e22 atoms/cm3 = 8.47 e28 atoms/m3 Magnitude of charge carrier: q = 1.602 e-19 C eCurrent: I = 10 A vd = I / (n|q|A) = (10 A) / [(8.47 e28 atoms/m3 )(1.602 e-19 C)(3.309 e-6 m2)] 1.602 ee(n|q|A) vd = 2.23 e-4 m/s eHow do the lights turn on so fast? Friday, 9 February 2007 5 Friday, 9 February 2007 Question Why do the lights turn on so fast? A. Electrons inside the wire travel near the speed of light B. Electric field inside the wire is established at the speed of light C. The wire is full of electrons D. A and B E. B and C 6 Current Density J Current I has some direction, but it is NOT a vector quantity! Question The electric field in a current carrying wire ... A. Is zero B. Is non-zero nonC. May be either zero or non-zero non- I Current Density: J = = n q vd A vd in - i^ ^ J in + i J = nqvd E ^ vd in + i ^ J in + i -q P e +q J Can be a vector because it describes the current at one particular location in a circuit. Conventional Current: The direction of the flow of positive charges! Friday, 9 February 2007 7 Friday, 9 February 2007 8 2 Resistance Va E Resistivity Experimentally, for conducting wires, we find: L Vb I e- Establish an electric field in a conductor. R= Va > Vb Because E-field points in Ethe direction of decreasing E-potential! L A is the length of the wire is the cross-sectional area of the material ( cross- L A V = Va - Vb = EL V Resistance: R = I is the resistivity of the material ( m ) is a property of the material, and is defined by: to the flow of charge) = E J E is constant in magnitude and direction! Units: ohm (1 = 1 V/A ) When the resistance does not depend on the voltage drop or the current, it is said to be an ohmic material! material! Ohm's Law: V = IR Ohm' Friday, 9 February 2007 For most conductors: 110-8 For glass (insulator): 1010 - 1014 Resistivities of materials can change with temperature: E = J R is constant! 9 (T ) = o [1 + (T - To )] R(T ) = Ro [1 + (T - To )] For most materials is positive! 10 Friday, 9 February 2007 Resistance of Non-Uniform Objects NonIf the area or resistivity is not constant over the length, then S = 4 +3x S Resistors in Parallel Typical R is big (k, (k M, G) ... G So V-drop across R >> V-drop between junction and top of each resistor! Must be @ same V E must be zero!?! dR = dL A of conductors ~ 10-8 m, so we need 108 m of wire for 1 resistance! 1 Current goes through the square crosscrosssection of this wire. Wire has a total length of L, and starts are x = 0. 0. Friday, 9 February 2007 R = dR = 0 L dx (4 + 3 x) 2 11 Friday, 9 February 2007 12 3 Resistors in Series An object that resists current flow is a resistor Energy in Circuits When charge travels from point a to point b, the energy lost is given by: "Equivalence" relationships for Resistors are exact opposite Equivalence" of those for Capacitors! Capacitors! Parallel: Series: Const. V The rate of energy lost is given by: Ceq, parallel = i Ci 1 1 Ceq, series Friday, 9 February 2007 Const. Q = i 1 Ci Const. V Const. I Req, parallel = i 1 Ri In general, Power Lost / Gain: For Ohmic resistors specifically: Req, series = i Ri 13 Friday, 9 February 2007 14 4 ...
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