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Current and Resistance in Conductors Lecture

This lecture covers the concepts of current, resistance, and conductors in electrical circuits. It discusses the flow of charge, the definition of current, and the relationship between current and potential difference. It also explores the factors that affect resistance in conductors.

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Current and Resistance in Conductors Lecture

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  1. Lecture 08 Current & Resistance October 3 or 5, 2005

  2. New Topic • Current and Resistance Commercial Resistors Color Coded

  3. Conductors • In the past we decided that in a conductor • The Electric Field is ZERO because we postulated that no charges were to move. • Static Situation • Any electric field must be at the surface • That field must be normal to the surface • Let’s look at another situation.

  4. Consider a conductor V1 V2 • The mobile electrons can “move” under the influence of an electric field. • We then have a “current” (to be defined) flowing in the wire. • But WAIT … how can we????? • Only if … Electric Field Walla ….. a CIRCUIT

  5. Symbol

  6. + - From the Past Q Flows and then stops. Vo

  7. Short! Vo A Different Situation circuit • Charge will begin to flow through the short. • Charge can flow back into the battery and discharge it. • Wire can get warm, emit light or even burn our (fuse). • The FLOW of charge is defined as a current.

  8. Current isa good thing

  9. Or a BAD thing It's the current that kills!

  10. Franklin’s Impact on Physics!!! ELECTRONS CURRENT • Positive charge will leave the battery from the positive terminal and flow through an external circuit to the negative terminal. • Electrons will go the other way. • Current is defined as the flow of POSITIVE CHARGE. • + charge does not normally flow in a wire.

  11. Definition • Current is the total amount of charge that flows through a “wire” in one second. • Current is measured in Coulombs per second. • A current of one coulomb per second is defined as an AMPERE. (Amp.)

  12. CONCISE DEFINITION: CURRENT Current will flow throughout the cross-section of the wire (usually). Current through aa’ is the same as the current through bb’ and cc’. What is DIFFERENT between aa’ and bb’ with respect to current?

  13. What’s Different?? i=5 amps CURRENT DENSITY A=.1 m2 A=0.05 m2 J=5 amps/.05 m2 = 100 amps/m2 J=5 amps / .1 m2 = 50 amps/m2

  14. Question: The current density in a wire of radius R is given by I0r. What is the total current flowing through the wire? Overhead Sol.

  15. Current Current can’t “pile up” at a point n a circuit.

  16. Example First introduction to Kirchoff’s Node Equation

  17. Consider 3A ^ 2A v 5A  6A 8 A

  18. + - Vo Question:A 5 Amp current is set up in a circuit for 6 minutes by a 6 Volt Battery. How much chemical energy is provided by the battery? CIRCUIT OF SOME SORT WORK (Energy) per unit Charge = qV

  19. wire i  V Definition Ohm’s Law High Low Current increases with Potential Difference (V)

  20. Observations • Wires and Resistors are made from conducting materials. • These materials have some fundamental properties associated with them. • Electrons are attached to atoms. • Outer electrons weakly bound • Small Force (Applied Electric Field) can easily push them. • They bump into things which retard their motion. • The more things that retard their motion, the more difficult it is to push a current via an applied potential difference. • Thus, the resistance goes up.

  21. What kinds of things cause resistance? • Sudden Constrictions in the conductor including bends! • Underlying structure- • Amorphous • Crystalline • Defects • Impurities • Thermal Collisions • Temperature

  22. Fundamental Property RESISTANCE vs. RESISTIVITY • Consider a wire made of some material. • Resistance is a property of the wire itself … the material and the shape. • New Quantity: • RESISTIVITY is a property of the material itself regardless of its shape.

  23. Consider our wire: • What would happen to the current if we • Increased the voltage? • Increased the Area? • Increased the length? L A V

  24. Summary r is the resistivity R is called the RESISTANCE and is measured in OHMS (W)

  25. Define CONDUCTIVITY s

  26. Resistivity – Ohm-Meters

  27. WIRES

  28. BACK TO OHM V=iR i=V/R

  29. Not EVERYTHING is a resistor The Semiconductor Diode

  30. Effect of Temperature

  31. Temperature Linear over a limited temperature range.

  32. Question-For an 18 gauge wire of length L to have a resistance of 1 ohm what must L be if the material is copper? L=46 meters! (d for 18 gauge is about 1 mm)

  33. A current of 6.5 Amps exists in a 9 Ohm resistor for 5 minutes. How many coulombs and how many electrons pass through the resistor in this time? Coulombs: 6.5 COULOMBS per Second for 5 minutes 6.5C x 5 min X 60 sec/min = 1950 coulombs Number of electrons = # coulombs / electron charge = 1950 / 1.6 x 10-19 = 1.22 x 10 +22

  34. Microscopic Theory

  35. J and E

  36. Consider a wire

  37. Micro-View “Resistivity” • depends on the material and is the mean time between collisions • ease of motion – mobility • resistance to motion - scattering

  38. + E L E C T R O N s V i - Power POWER Battery supplies energy to the resistor which, in turn, dissipates it in the form of heat. Work done on charge Q = Q x V REMEMBER: P=iV and P=i2R

  39. ENGINEERED MATERIALS!!! Semiconductors The Spectrum of Conductors

  40. When 105 volts are applied across a wire that is 12 meters long and has a 0.30 mm radius, the current density us 1.7 x 10 4 A/m2. What is the resistivity of the wire?? From the current density we can find the CURRENT. i=JA = 1.7 x 104 amp/m2 X (p X 0.32) mm2 X (1m/1000mm)2 I = 4.8 ma R= V/i = 105 volts / (4.8 x 10-3) amps = 2.18 x 104 ohms r = 2.18 x 104 ohms x 3 x 10-7 m2 / 12m = 0.005 ohm-meters

  41. copper 12 volts 0 volts The figure below gives the electrical potential V(x) along a copper wire carrying a uniform current, from a point at higher potential (x=0m) to a point at a lower potential (x=3m). The wire has a radius of 2.45 mm. What is the current in the wire? What does the graph tell us?? *The length of the wire is 3 meters. *The potential difference across the wire is 12 m volts. *The wire is uniform. Let’s get rid of the mm radius and convert it to area in square meters: A=pr2 = 3.14159 x 2.452 x 10-6 m2 or A=1.9 x 10-5 m 2 Material is Copper so resistivity is (from table) = 1.69 x 10-8 ohm meters

  42. We have all we need….

  43. R1 R2 V1 V2 V i i Series Combinations

  44. R1, I1 R2, I2 V Parallel Combination??

  45. What’s This??? In Fig. 28-39, find the equivalent resistance between points (a) F and H and [2.5](b) F and G. [3.13] ?

  46. The current density across a cylindrical conductor of radius R varies according to the equation J = J0(1 - (r/R)), where r is the distance from the central axis. Thus the current density is a maximum J0 at the axis (r = 0) and decreases linearly to zero at the surface (r = R). Calculate the current in terms of J0 and the conductor's cross-sectional area A = R2.

  47. That’s it for Resistance Next Time Electric Circuits

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