PHYS219 Fall semester 2014 Lecture 07: Current Flow Dimitrios Giannios Purdue University

So far, we have studied static charges at well defined positions → understanding of electrostatic forces, electric fields, and potential differences. What happens when charge is permitted to move? What rules govern the flow of charge? Electro Dynamics The Study of Charge in Motion

Define Electric Current I as the rate of flow of net charge through a surface. The charge can be carried by anything that has a net charge: electrons, ions, molecules, particles, etc.. Surface +q 1 +q2+q2 -q 3 -q 4 +q 5 ΔtΔt Clock  Current need not be confined to wire.  Units of I: [C/s = Ampere = A]  Note that mathematically, -q moving in +x direction is equivalent to +q moving in –x direction +x 0 -x I=I= ΔtΔt

When current flows through a wire Definition of Conventional Current I By definition, the direction of current flow for either case is the same. I

Current – Orders of Magnitude 1 x A = 1 pA (about 10 7 e - /s) 10 x A = 10 nA (leakage current in transistors) 1 x A = 1  A (typical input current to IC) 1 x A =1 mA (humans can feel this) ~0.02 A = 20 mA (muscle contraction) 50 x A = 50 mA (painful to humans) ~0.1 A = 100 mA (death) ~ 1 A (current thru 100 W light bulb) A (lightning bolt)

What Drives Current Flow? A potential difference develops across the terminals of a battery EMF = ElectroMotive Force =

Resistance to Flow: The ratio of the potential energy difference across a conductor to the current flowing through it. Analogy to Water Flow What factors limit the flow of water? What factors limit the flow of charge?

Currents on Earth and the universe Currents are not only on wires! currents require free charges  Plasma (gas at temperature of million-billion K!) Fusion Device (Tokamak) Astrophysical Currents (and instabilities!) I

Microscopically, how does the current flow in a wire? Atom 1 Atom 2 Atom 3 Atom 4 Atom 5 Atom 6 A few nanometers (1 nm = 1 x m) I vdvd Net drift velocity of electron due to applied electric field I E= -Δ V/ Δ s E E FEFE

Current and Drift Velocity Current is related to the drift velocity where: A= wire cross section, n= number density of electrons, I=current For a household size copper wire carrying 1 A of current, the drift velocity is about m/s! There is no perceptible time delay between when you push a switch and when the light comes on The speed of the electric current is equal to the speed of electromagnetic radiation in the wire This is nearly the speed of light

UNITS : Ohm’s Law ΔVΔV I R = V/A = Ohm [Ω] I

current flows and electrical resistance 360 mA 9.0 V

What determines resistance R for a wire? Units: L (m); A(m 2 ); ρ(Ω ∙ m); R(Ω) (constant over entire length)

Electrical Resistivity (ρ) Some materials, like metals, offer little resistance to current flow. Other materials, like plastic, offers high resistance to current flow. Resistivity is used to quantify how much a given material resists the flow of current. Resistivity is a property of a material.

Distinguish between resistivity and resistance Resistivity is a property of a material. Resistance of a component depends on BOTH geometry as well as the resistivity of the material from which it is made. R=ρL/A

A=π(d/2) 2 A=d 2 A=½ base*height =½d ∙ d√3/2=d 2 √3/4 d d d√3/2 Three wires, same length & material different cross-sections d d L 60 ◦

Determine the resistance of a 100 meter length of 12 AWG (2.052 mm diameter) solid wire made of the following materials: a.copper (resistivity = 1.67x10 -8 Ωm): b.aluminum (resistivity = 2.65x10 -8 Ωm) c.iron (resistivity = 9.71x10 -8 Ωm) American Wire Gauge (AWG) Can a copper wire and an aluminum wire of the same length have the same resistance? R iron = ρ Fe L/A = (9.71 x Ω m) 100m/(3.31 x m 2 ) = 2.93 Ω R Aluminun = ρ Al L/A = (2.65 x Ω m) 100m/(3.31 x m 2 ) = Ω R Copper = ρ Cu L/A = (1.67 x Ω m) 100m/(3.31 x m 2 ) = Ω Area = π R 2 = π ( m/2) 2 =3.31 x m 2

2L 2r 4r A wire has a resistance R. If the length of the wire is doubled and the radius is also doubled, what is the new resistance? L 1 2