# Physics 2102 Spring 2002 Lecture 8 - LSU Resistance Is Futile! Physics 2113 Jonathan Dowling Physics 2113 Lecture 19: MON 02 MAR Current & Resistance I Georg Simon Ohm (1789-1854) Electric Current dq C i = [ Ampere] =[ A]

dt s Current i is the Rate (charge/second) charge passes by a poin ositive Current is Direction of Positive Charge Flow! 26.2: Electric Current: The figure shows a section of a conductor, part of a conducting loop in which current has been established. If charge dq passes through a hypothetical plane (such as aa) in time dt, then the current i through that plane is defined as: The charge that passes through the plane in a time interval extending from 0 to t is: Under steady-state conditions, the current is the same for planes aa, bb, and cc and for all planes that pass completely through the conductor, no matter what their location or orientation. The SI unit for current is the coulomb per second, or the ampere (A): 26.2: Electric Current, Conservation of Charge, and Direction of Current:

Kirchoffs Law: Sum of Total Current Into a Junction Must Equal Sum of Total Current Out: Conservation of Charge! 26.2: Electric Current, Conservation of Charge, and Direction of Current: Fill in the blanks. Think water in hose! 2 + 3 =5 1+ 2 =3 3 + 2 =5 2 + 4 =6

6 + 2 =8 3A 2A Example, Current is the Rate at which charge passes through a point: Water is Neutral. What is the Current of + Charge? Current Density J and Drift Speed vd The current is the flux of the current density! If surface is perpendicular to a constant electric field, then i=JA, or J=i/A dA

J Ampere [J ] = m2 Units: E i Drift speed: vd :Velocity at which electrons move in order to establish a current. Charge q in the length L of conductor:q =( n A L) e L

n =density of electrons, e =electric charge A E i L t= vd q n AL e i= = =n Aevd L t vd vd =

i J = n Ae n e + + + + - ll quantities defined in terms of + charge movement! (a) right (b) right (c) right

(d) right Example, In a current, the conduction electrons move very slowly.: If electrons move so slowly, Why does a light come on the instant You throw the switch? Example, Current Density, Uniform: SP-PG-387 What is total net current? 1 4 3 4

Atot i = 43 itot itot = 43 i =2.53A Atot IPPC: Let the current density J remain constant. What happens to the current if we: 2 i A R A = 43 Atot

i 4i (a)Double the Radius? i 2i (b) Double the Area? i i (c) Double the Length? Example, Current Density Nonuniform, cont.: Integration with Cylindrical Shells dr ienc JA unless J is constant! J(r) = ar2 is NOT a constant!

i L dA 2 A =p r dA =2p rdr r2 2 4 2 itot =ar 2p rdr =ap r / 2

0 r11 r22 2 4 1 icore =ar 2p rdr =ap r / 2 0 C/s m 4 m4 1

ap 4 4 ishell =ar 2p rdr = ( r2 - r1 ) 2 r11 2