Current in a Wire
- Current is a measure of the rate at which charge is flowing past some point in a wire.
Definition: Instantaneous Current
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SI: Ampere = Amp = A = Coul/sec = C/s |
1 Amp 
6.242x10 18 electrons per second
Drift Velocity and Current
- When a Voltage is applied across the ends of a wire, an Electric Field is created inside the wire, E = V/L where L is the length of the wire.
- In a vacuum the electric field would cause a charge to accelerate. In a wire, collisions of the conduction charges with impurities, imperfections, and vibrations of the atomic lattice causes the motion of the conduction charges to be slowed down. This represents a loss of energy which is dissipated as heat.
- Over a wide range of conditions, the flow of the charges quickly achieves a steady state value and remains constant. The "average speed" at which the "free" charges are moving in the wire is called the drift velocity vd.
- The charge carriers in a wire are normally electrons. The number of conduction electrons "free" to participate in the current flow depends upon the atomic structure of material making up the wire. Conductors have many electrons that are able to participate, where as insulators have few free electron. Semiconductors are materials that lie somewhere between these two extremes.
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- The current in a wire can be expressed as function of the number of charge carriers/volume, the magnitude of the charge carriers, the drift velocity of the charge carriers, and the cross-sectional are of the wire,
| vd = |
Drift Velocity (SI: m/s) |
| rn = |
Number Density - Charges per unit Volume (SI: #/m 3)
(The text uses n for this symbol, don't confused it with # moles) |
| q = |
Magnitude of the charge on each moving charge (SI: C)
(Typically q = e = 1.602x10 -19 C, charge on an electron) |
| A = |
Cross-sectional Area perpendicular to the flow. (SI: m 2) |
Derivation:
Look at a volume V = A L of the wire whose length L is equal to the distance a charge carrier would move at the drift velocity in one second, L = vd (1 s). We can determine the charge Q in this volume,
Q = (charge on a charge carrier)x(number of charge cariers per unit volume)x(volume) = q rn A vd
In one second this amount of charge will flow through the volume. Since the current is charge flow per second this is also the current.
- Note that the thermal motion of the conduction electrons (~ 1000 km/s) is many times larger than typical drift velocity (~ .1 mm/s).