Question of the day What additional quantities are necessary to describe the behavior of an electric field when the charge moves?

Current Electricity made a giant leap in 1800 when Volta invented the electric cell and the battery (of cells). For the first time investigators had a source of steady electric current. Volta demonstrates the battery to Napoleon.

Current A current is any motion of charge from one region to another. Conventional current is treated as a flow of positive charges. A current can be produced by positive or negative charge flow. In a metallic conductor, the moving charges are electrons — but the current still points in the direction positive charges would flow.

Signs of charge carriers In general, a conductor may contain several different kinds of moving charged particles. An example is current flow in an ionic solution. In the sodium chloride solution shown, current can be carried by both positive sodium ions and negative chlorine ions The total current I is found by adding up the currents due to each kind of charged particle.

Current density We can define a vector current density that includes the direction of the drift velocity: The vector current density is always in the same direction as the electric field, no matter what the signs of the charge carriers are.

Current and Drift Velocity This table gives n for various metals. If the electrons have an average drift speed vd, then on the average in a time interval Dt they would travel a distance Dx in the wire, where Dx = vd Dt. If the wire has cross sectional area A and there are n electrons per unit volume in the wire, then the number of electrons moving through the cross sectional area in time Dt is Ne = nA Dx = nAvdDt. Therefore, I = neAvd

Resistivity Conductors Semiconductor: Insulators The resistivity of a material is the ratio of the electric field in the material to the current density it causes: The conductivity is the reciprocal of the resistivity. Substance ρ (Ω ∙ m) Copper 1.72 ×10−8 Gold 2.44 ×10−8 Lead 22 ×10−8 Pure carbon (graphite) 3.5 ×10−5 Glass 1010 – 1014 Teflon >1013 Wood 108 – 1011 Conductors Semiconductor: Insulators

Conductivity and Resistivity The current density J = nevd is directly proportional to the electron drift speed vd. The microscopic conduction model gives vd = etE/m, where t is the mean time between collisions. Therefore: The quantity ne2t/m depends only on the properties of the conducting material, and is independent of how much current density J is flowing. This suggests a definition: This result is fundamental and tells us three things: Current is caused by an E-field exerting forces on charge carriers; (2) Current density J and current I=JA depends linearly on E; (3) Current density J also depends linearly on s. Different materials have different s values because n and t vary with material type. Units: ohms = W = Nm2/CA = Nm2s/C2

The Current Density in a Wire Example: A current of 1.0 A passes through a 1.0 mm diameter aluminum wire. What is the drift speed of the electrons in the wire?

Example: The Electric Field in a Wire A 2.0 mm diameter aluminum wire carries a current of 800 mA. What is the electric field strength inside the wire? The electric field strength is

Electrons still do a random walk with their thermal energy when they are pushed along a conducting wire by an electric field. They merely “drift” down the wire as they are randomly bounced around by collisions. Even though the electrons move slowly down the wire, the electric field E moves at speed of light in wire, so you don’t have to wait for the lights to come on…the electrons throughout the wire begin moving almost instantaneously. These collisions are the fundamental cause of resistance and heat up the wire.

Circuit boards and resistivity The copper “wires,” or traces, on this circuit board are printed directly onto the surface of the dark-colored insulating board. Even though the traces are very close to each other, the board has such a high resistivity that essentially no current can flow between the traces.

Resistivity and temperature The resistivity of a metallic conductor nearly always increases with increasing temperature. Over a small temperature range, the resistivity of a metal can be represented approximately: Material α [(°C)−1] Aluminum 0.00039 Carbon (graphite) −0.0005 Copper 0.00393 Iron 0.0050 Lead 0.0043 Silver 0.0038 Tungsten 0.0045

Resistivity and temperature The resistivity of graphite (a semiconductor) decreases with increasing temperature, since at higher temperatures, more electrons “shake loose” from the atoms and become mobile. Measuring the resistivity of a small semiconductor crystal is a sensitive measure of temperature; this is the principle of a type of thermometer called a thermistor.

Superconductivity Some materials show a phenomenon called superconductivity. As the temperature decreases, the resistivity at first decreases smoothly, like that of any metal. Below a certain critical temperature Tc a phase transition occurs and the resistivity suddenly drops to zero. Once a current has been established in a superconducting ring, it continues indefinitely without the presence of any driving field.

Resistance and Ohm’s law The resistance of a conductor is The potential across a conductor is given by Ohm’s law: V = IR.

Resistors and Ohm’s Law Often called Ohm’s Law

Example: The Current in a Wire What is the current in a 1.0 mm diameter 10.0 cm long copper wire that is attached to the terminals of a 1.5 V battery?

Resistors are color-coded for easy identification This resistor has a resistance of 5.7 kΩ with a tolerance of ±10%.

Ohmic resistors For a resistor that obeys Ohm’s law, a graph of current as a function of potential difference (voltage) is a straight line.

Nonohmic resistors In devices that do not obey Ohm’s law, the relationship of voltage to current may not be a direct proportion, and it may be different for the two directions of current. Important non-ohmic devices: Batteries, where DV=E is determined by chemical reactions independent of I; Semiconductors, where I vs. DV can be very nonlinear; Light bulbs, where heating changes R; Capacitors, where the relation between I and DV differs from that of a resistor.

Light Emitting Diodes (LEDs)