ECE 106 - Current and Resistance

Current density J→ =

J = I / A = nqv

n = number density of electrons

q = charge per carrier

v = ΔX / Δt
A = area

Conductivity =

J / E = σ (constant)

→ J = σE

σ depends ONLY on the medium, NOT on the conductor's dimensions

Conductivity and resistivity relation =

σ = 1 / ρ

(σ depends ONLY on the medium, not the conductor's dimensions)

Resistance of a conductor =

R = (ΔX)/(σA)

ΔX = length

σ = conductivity

A = cross-section

Why does current direction matter when calculating resistance =

resistance is dependent on ΔX and A (area)

• these will change based on direction of current

what is resistance in series and in parallel =

series:

• R_tot = R_{1 +} R₂

• Both materials have DIFFERENT voltage drop

parallel:

• 1/R_tot = 1/R₁ + 1/R₂

• Both materials have SAME same voltage drop

integral form of current =

I = ∬J⋅dS^→

• J = current density