Physics 2113 Lecture 17 Resistance Is Futile! Current & Resistance I Jonathan Dowling Resistance Is Futile! Physics 2113 Lecture 17 Current & Resistance I Georg Simon Ohm (1789-1854)

Relation Between E and V Bring imaginary + test charge q0 = 1C in from infinity! Since V is the anti-derivative of E then E is the Derivative of V.

SERIES OR PARALLEL? PAR-V VOLTAGE THE SAME / SERI-Q CHARGE THE SAME Series if plates break the circuit into islands. Parallel if plates break the circuit into half of equal voltage.

SERIES OR PARALLEL?

SERIES OR PARALLEL?

SERIES OR PARALLEL? SLIDE RULE: CAN MOVE ANY CAPACITOR AROUND A WIRE BUT NOT PAST ANOTHER WIRE OR A 3-POINT JUNCTION.

Electric Current Current i is the Rate (charge/second) charge passes by a point. Positive Current is Direction of Positive Charge Flow!

ICPP: What is Direction and Magnitude of each current?

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):

Sum of Total Current Into a 26.2: Electric Current, Conservation of Charge, and Direction of Current: Kirchoff’s Law: Sum of Total Current Into a Junction Must Equal Sum of Total Current Out: Conservation of Charge! WHAT GOES IN MUST COME OUT! THINK OF GALLONS PER SECOND!

First do junctions that have at least two numbers given. 26.2: Electric Current, Conservation of Charge, and Direction of Current: Fill in the blanks. Think water in hose! First do junctions that have at least two numbers given.

Current Density J and Drift Speed vd The current is the flux of the current density! E i J dA If surface is perpendicular to a constant electric field, then i=JA, or J=i/A Units: Drift speed: vd :Velocity at which electrons move in order to establish a current. E i L A Charge q in the length L of conductor: n =density of electrons, e =electric charge

All quantities defined in terms of + charge movement! (a) right (b) right (d) right (c) 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?

IPPC: Let the current density J remain constant IPPC: Let the current density J remain constant. What happens to the current if we: Double the Radius? (b) Double the Area? (c) Double the Length?

What is total net current? Example, Current Density, Uniform: SP-26.02 PAGE 750 What is total net current?

Example, Current Density Nonuniform, cont.:

Integration with Cylindrical Shells ienc ≠ J•A unless J is constant! J(r) = ar2 is NOT a constant! i L dA