Current in a Conductor | CAIE 9702 Paper 2 Notes

Paper 2

Physics9702

Current in a Conductor

A current depends on how many mobile carriers are available, how much charge each carrier has, the wire area and their mean drift velocity.

The carriers drift slowly; the circuit responds quickly because the electric field is established throughout the complete circuit.

Build the current relation

In time $t$ , carriers with mean drift velocity $v$ move through a length $vt$ .
A wire of cross-sectional area $A$ therefore supplies carriers from a volume $Avt$ .
If there are $n$ carriers per cubic metre, the charge passing is $nAvtq$ . Dividing by time gives the current.

I=nAvq

Symbols

$I$ = current (A)
$n$ = number density of mobile charge carriers (\text{m}^{-3})
$A$ = cross-sectional area (\text{m}^2)
$v$ = mean drift velocity (\text{m s}^{-1})
$q$ = charge of one carrier (C)

Number density is the number of mobile carriers per unit volume. It is not the total number of carriers in the whole wire.

Predict before calculating

With $n$ , $A$ and $q$ fixed, increasing $I$ increases $v$ .
With $I$ , $n$ and $q$ fixed, decreasing $A$ increases $v$ .
With $I$ , $A$ and $q$ fixed, decreasing $n$ increases $v$ .
If more than one factor changes, combine all factors before deciding what happens to $v$ .

current I1.0 Aarea A1.0 mm²density n8.5

n is in units of 10²⁸ per m³ (copper ≈ 8.5)

v = 0.074 mm/s·time to drift 1 metre ≈ 3.8 hours

Common mistake

Convert square millimetres by squaring the conversion:

1\ \text{mm}^2=1.0\times10^{-6}\ \text{m}^2

Your turn9702/21/M/J/25 Q6(a)(ii)

A wire carries 1.2 A. Its area is $4.7\times10^{-7}\ \text{m}^2$ , its number density is $8.5\times10^{28}\ \text{m}^{-3}$ and the carrier charge is $1.60\times10^{-19}\ \text{C}$ . Calculate the mean drift velocity. [2] (9702/21/M/J/25 Q6(a)(ii))

Show worked answer

Rearrange to $v=I/(nAq)$ .
Substitute all values in SI units.

Answer

v=1.9\times10^{-4}\ \text{m s}^{-1}