Skip to main content

Mathematics for Physics

22 Current

A rate of electric charge flow past a point that is used to measure how much charge passes through a wire or region per unit time.

Note: Also called electric current.

definition [d] (Current = Electric Current) From Knight: if \(Q\) is the total amount of charge that has moved past a point in the wire, we define the current \(I\) in the wire to be the rate of charge flow:

  • \(I \equiv \dfrac{dQ}{dt}\) .

where

  • \(I\) is the electric current.
  • \(Q\) is the charge that has passed the point.
  • \(t\) is time.

22.1 Elementary Example

22.1.1 Simple

If \(4\,\mathrm{C}\) pass a point in \(2\,\mathrm{s}\), the average current is

\[ I = \dfrac{\Delta Q}{\Delta t} = 2\,\mathrm{A} \]

where

  • \(I\) is the current in amperes.

22.1.2 General

A steady current of \(3\,\mathrm{A}\) for times \(t = 1,2,3\,\mathrm{s}\) moves charges

\[ Q(t) = It = 3t\,\mathrm{C} \]

where

  • \(Q(t)\) is the total charge that has passed by time \(t\).