The Physics
Hypertextbook
Opus in profectus

Electric Current

Summary

• Electric current is the rate at which charge flows through a surface.
• Electric current is often just called current.
• As a scalar, current has magnitude only.
• The symbol for current is I (italic) from the intensity of a current.
• In equation form, current can be written as…
average current instantaneous current
 Iave = ∆q ∆t
I =   lim ∆t→0
q  =  dq
t dt
Where…  I = electric current [A] ∆q, dq = charge passing through some area [C] ∆t, dt = interval, instant of time [s]
• The SI unit of current is the ampère [A].
• An ampère is a coulomb per second.  A = C s
• The ampère is one of the seven base units of the International System of Units.
• The unaccented spelling ampere is also acceptable in written English.
• The shortened form amp is often acceptable or even preferred.
• The SI unit of charge is the coulomb [C]
• The coulomb is a derived unit.
• One coulomb is the amount of charge transferred by one ampère of current in one second of time [C = A s].
• Current density is a quantity related to electric current.
• The symbol for current density is J (bold).
• As a vector, current density has magnitude and direction.
• By definition, current density is the product of charge density (ρ) and velocity (v).
• The magnitude of current density is also equivalent to the ratio of current (I) to area (A).
• In equation form, current density can be written as…
vector definition magnitude equivalent
J = ρv  J = I A
Where…  J, J = current density [A/m2] as a vector or its scalar magnitude I = electric current [A] ρ = charge density [C/m3] v = drift velocity [m/s] A = area [m2]
• The SI unit of current density is the ampère per square meter [A/m2].
• Microscopic description of current
• The macroscopic phenomenon of electric current can be described by the net motion of microscopic charged particles.
• In equation form, the microscopic description of current and current density can be written…
microscopic current microscopic current density
I = nqAv J = nqv
Where…  I = electric current [A] J = current density [A/m2] n = particle density [particles/m3] q = charge per particle [C] v, v = drift velocity [m/s] A = area [m2]