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]