Lesson 5 Current and Resistance Batteries Current Density

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

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

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

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

Flow of Charge

Current Picture I

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

Current Picture Definition II

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

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

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

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

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

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

Power = rate of doing work by applied force d. U = d. Q = Power = V IV dt dt C Nm Nm = [Power ]=[I][V ] = AV = s C s J= ) W (Watts s

Ohmic Materials I

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

Resistivity

Picture l I V+ a E V-

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

Integral Formula

Classical Electrical Conduction Microscopic Theory of Electrical Conduction

Random Walk

Picture

Charge in Volume DV DQ = n. A D x q = n. Av d Dt q n = number of charge carriers per unit volume Definition of Variables A cross sectional area = q = amount of charge on each carrier D x = average distance moved in time D t after collision v d = drift velocity

Equations I Þ DQ x D q = n. A Dt Dt d. Q = I = n. Av d q dt Þ J = nvd q J Þ = vd nq

acceleration of charge q in field E q a = E m • Let t = average time between collisions • at each collision charge carrier forgets drift velocity , so we can take initial drift velocity = 0 and just before collisions æ q ö q t÷E vd = a t = Et = ç èm ø m Equations II vd = J q = t E nq m nq t Þ J = E m 2 nq t Þ s = m 2

Temperature Effects 1 m r= = 2 s nq t As temperature increases t decreases thus r increases r(T) = r 0 [1+a(T - T 0 )] 1 dr a=r = Temperature Coefficient of Resistivity 0 d. T

Temperature Effects r(T) = r 0 [1+a(T - T 0 )] 1 dr a=r = Temperature Coefficient of Resistivity 0 d. T Equation Thus R (T ) = R 0 [1 + a(T - T 0 ) ]