Chapter 30: Notes Sheet

30.1 The Electron Current

Some vocabulary/ concepts:

- Current is the flow of charge through a conductor. 
- Charge carriers are the charges that move in a conductor.

Electrons are the charge carriers in metals​

- The electron drift speed, v_d, is the net motion caused by pushing electrons through a conductor with an electric field.
- The electron current, i_e, is the number of electrons per second that pass through a cross section of a conductor.
- The number of electrons, N_e, is literally the quantity of electrons that pass through the cross section.
- The number density, n_e, is the quantitative density of conduction electrons per volume in the conductor.

Equations:

N_e = i_e⋅Δt                                                 (30.1)
N_e = n_e⋅V = n_e⋅A⋅Δx = n_e⋅A⋅v_d⋅Δt          (30.2)
i_e = n_e⋅A⋅v_d                                             (30.3)

Tables/ Useful info:

30.2 Creating a Current

Some vocabulary/ concepts:

- An electron current is a nonequilibrium motion of charges sustained by an internal electric field.
- A nonuniform distribution of surface charges along a wire creates a net electric field inside the wire that points from the more positive end of the wire toward the more negative end of the wire. This is the internal electric field E that pushes the electron current through the wire. 
- Collisions transfer much of the electron's kinetic energy to the ion and thus to the thermal energy of the metal. This transfer is the 'friction' that raises the wire's temp.
- The magnitude of the electron's average velocity, due to the electric field, is the drift speed of the electron.
- The mean time between collisions, Δt, is designated as τ.
- The electron current is directly proportional to the electric field strength.

Equations:

v_d = e⋅τ⋅E/m                (30.7)
i_e = n_e⋅e⋅τ⋅A⋅E/m        (30.8)

30.3 Current and Current Density

Some vocabulary:

- The Ampere is the SI unit for current. It is equivalent to a Coulomb per second.
- The direction of current is defined to be the direction in which positive charges seem to move. - But the direction of the current I in a metal is opposite the direction of motion of the electrons
- The current density is current per square meter of cross section in the conductor
- The rate of electrons leaving a lightbulb (or any other device) is exactly the same as the rate of electrons entering the bulb. AKA, current doesn't change. → Law of conservation of current

Equations:

I = dQ/dt                                                   (30.9)
Q=I⋅Δt                                                      (30.10)

I = Q/Δt = eN_e/Δt = e i_e                             (30.11)
Current Density ≡ J = I/A = n_e⋅e⋅v_d          (30.13)
ΣI_in = ΣI_out                                                (30.14)

30.4 Conductivity and Resistivity

Some vocabulary/ concepts:

- The conductivity of a material is a characteristic independent of temperature or size. It is designated with the greek letter sigma, σ. it has units of Ω^-1m^-1
- The resistivity is the inverse of conductivity and is designated with the Greek letter rho, ρ. It has units of Ωm

Equations:

J = n_eev_d = n_ee²τE/m          (30.15)
σ = n_ee²τ/m                        (30.16)
J = σE                                  (30.17)
ρ = 1/σ = m/[n_ee²τ]            (30.18)

Tables/ Useful Info:

30.5 Resistance and Ohm's Law

Some vocabulary/ concepts:

- The current is proportional to the potential difference between the ends of a conductor.
- Resistance is a property of a conductor and depends on length, diameter, and resistivity of the material make-up. The units for resistance are ohms, Ω. 1 Ω = 1 Volt/Ampere = 1 V/A
- A battery is a source of potential difference.
- An ideal wire has no resistance, or R = 0 Ω
- Resistors are poor conductors, and are used to limit current within circuits. 
- Insulators are materials that barely conduct any electricity.
- An ideal insulator has infinite resistance, or R = ∞ Ω, and no electricity is conducted through it. 

Equations:

E = ΔV/Δs = ΔV/L         (30.19)
I = JA = AσE = AE/ρ      (30.20)
I = AΔV/(ρL)                 (30.21)
I = ΔV/R                       (30.23)

Ohm's Law: V = IR