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Lesson 5 Current and Resistance Batteries Current Density Electron Drift Velocity Conductivity and Resistivity Resistance and Ohms’ Law Temperature Variation of Resistance Electrical Power and Joules Law Classical Model of Conduction in Metals Lesson 5

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Electrical Resistance is “friction” to the flow of electric charge Observed in Conductors and Non Conductors Not found in Super Conductors Electrical Resistance

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Charge Pump I I + - Load Resistance Capacitor will send current through load resistance and loose charge

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Charge Pump I I + - Load Resistance Battery will send current through load resistance and not loose charge Charge in battery is regenerated by Chemical reactions

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Flow of Charge

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I Current Picture

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Current is the rate of Flow of positive charge through whole cross sectional area of conductor Current Picture Definition I

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Current Picture Definition II

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Current is Conserved I1I1 I2I2 I1I1 I 1 +I 2 Conservation of Current

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Flowing charge experiences friction Work must be done to overcome friction Need driving force, hence need Electric Field Potential Difference Driving force for Current

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Electrical Resistance= Potential Difference Current R V I R V I V A (Ohm) SI units

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I-V plots I V I V slope constant = 1/R slope not constant Ohmic MaterialNon Ohmic Material V-I plots

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Ohmic Materials Resistance I V RI Ohms Law R V I constant

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Non Ohmic Materials R is not Constant, but varies with current and voltage Resistance II

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Power = rate of doing work by applied force Power = dU dt dQ dt V IV Power I V AV C s Nm C s J s W (Watts )

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Ohmic Materials I

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For Ohmic Materials Resistance is proportional to length of conductor Resistance is inversely proportional to the cross sectional area of the conductor Ohmic Materials II

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Resistivity

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Picture I V+V+ V-V- l E a

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|V| V V El I V R l a Ea Divide by Area Current Density magnitude = Current per cross sectional area J I a E E = conductivity 1 Current Density

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Integral Formula

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Classical Microscopic Theory of Electrical Conduction Electrical Conduction

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Random Walk

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Picture

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Definition of Variables Charge in Volume V Q nA x q nAv d t q n number of charge carriers per unit volume A cross sectional area q amount of charge on each carrier x average distance moved in time t after collision v d drift velocity

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Q t nAq dQ dt I nAv d q J nv d q J nq v d Equations I x t

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Equations II acceleration of chargeq in field E a q m E Let average time between collisions at each collision charge carrierforgets drift velocity, so we can take initial drift velocity=0 and just before collisions v d a q m E q m E v d J nq q m E J 2 m E 2 m

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Temperature Effects 1 m nq 2 As temperature increases decreases thus increases T 0 1 T T 0 1 0 d dT Temperature Coefficient of Resistivity

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Temperature Effects T 0 1 T T 0 1 0 d dT Temperature Coefficient of Resistivity Thus RT R 0 1 T T 0 Equation

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