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

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

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

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

Flow of Charge

I Current Picture

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

Current Picture Definition II

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

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

Electrical Resistance= Potential Difference Current R  V I R   V  I   V A  (Ohm) SI units

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

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

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

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 )

Ohmic Materials I

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

Resistivity

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

|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

Integral Formula

Classical Microscopic Theory of Electrical Conduction Electrical Conduction

Random Walk

Picture

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

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

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

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

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