Definition

Current

I \equiv \frac{d Q}{d t}

Statement

Charge per unit time through a surface.

Symbols and units

When it applies

Any conductor, any carrier.

Derivation

Count the charge crossing a section in a time interval:

I_{avg} = \frac{Δ Q}{Δ t}

Shrink the interval for the instantaneous value:

I = \frac{d Q}{d t}

Worked examples

Electrons per second at 1 A

\frac{I}{e} = \frac{1.0}{1.6 \times 1 0 ^{- 19}} = 6.2 \times 1 0^{18} s^{- 1}

Charge appears continuous at everyday scale despite being quantized.

Watch out for

Current is not used up along a wire. The same current enters and leaves a lamp; what gets used up is energy.

Connects to