Question

A uniform copper wire carries a current $i$ amperes and has $p$ carriers per metre. The length of the wire is $l$ metres and its cross-section area is s metre. If the charge on a carrier is $q$ coulombs, the drift velocity in $m{s}^{-1}$ is given by

• A. $i/lsq$
• B. $i/psq$
• C. $psq/i$
• D. $i/pslq$

Answer 1

The correct option is B $i/psq$

The current flowing through the wire is given by
$I=neAv$
Where I = current
n = charge carrier current density
e = charge on the carriers
A = cross sectional area
v = drift velocity
In the above example
I = current = i
n = charge carrier current density = p
e = charge on the carriers = q
A = cross sectional area = s
v = drift velocity = v
hence $i=pqsv$
$\therefore v=\frac{i}{pqs}$