AcademyCurrent and Resistance
Academy
Electric Current
Level 1 - Physics topic page in Current and Resistance.
Principle
Electric current measures the rate at which charge crosses a chosen surface.
Notation
\(I\)
electric current
\(\mathrm{A}\)
\(\Delta Q\)
charge crossing a surface
\(\mathrm{C}\)
\(dQ\)
small amount of charge crossing a surface
\(\mathrm{C}\)
\(\Delta t\)
time interval
\(\mathrm{s}\)
\(\vec J\)
current density
\(\mathrm{A\,m^{-2}}\)
\(A\)
cross-sectional area
\(\mathrm{m^{2}}\)
Method
Derivation 1: Define current from charge flow
Choose a surface in a wire or device. Current counts signed charge crossing that surface per unit time.
Average current
\[I_{\mathrm{avg}}=\frac{\Delta Q}{\Delta t}\]
Instantaneous current
\[I=\frac{dQ}{dt}\]
Ampere
\[1\,\mathrm{A}=1\,\mathrm{C\,s^{-1}}\]
Derivation 2: Current direction is conventional
Current direction is defined as the direction positive charge would move. In metals, mobile electrons drift opposite the conventional current.
Positive carriers
\[q>0\Rightarrow \vec v_{\mathrm{drift}}\parallel\vec I\]
Electron carriers
\[q<0\Rightarrow \vec v_{\mathrm{drift}}\ \text{opposite conventional current}\]
Derivation 3: Spread current over an area
If current is distributed uniformly through a cross-section, current density is current per area.
Uniform current density
\[J=\frac{I}{A}\]
Recover current
\[I=JA\]
Rules
These are the compact current definitions.
Average current
\[I_{\mathrm{avg}}=\frac{\Delta Q}{\Delta t}\]
Instantaneous current
\[I=\frac{dQ}{dt}\]
Current density
\[J=\frac{I}{A}\quad\text{for uniform flow}\]
Ampere
\[1\,\mathrm{A}=1\,\mathrm{C\,s^{-1}}\]
Examples
Question
A charge of
\[18\,\mathrm{C}\]
crosses a wire cross-section in \[6.0\,\mathrm{s}\]
Find the average current.Answer
\[I=\frac{\Delta Q}{\Delta t}=\frac{18}{6.0}=3.0\,\mathrm{A}\]
Checks
- Current needs a chosen surface and a direction convention.
- Conventional current follows positive charge motion.
- Electron drift in a metal is opposite conventional current.
- Current density is a vector in general, even though many wire problems use its magnitude.