Question

Derive the relation between current and drift velocity and write all terms

Answer 1

Hint: Rate of flow of charge is considered current. Here electrons are passing through a cross section in a particular direction. We consider the flow of current in direction opposite to electron flow as electrons have negative charge. Amount of current is given and time of flow of electrons in filament is also given. From this we can find out the time rate of flow of charge

Formula used:
$i = \dfrac{{dq}}{{dt}}$

Complete step-by-step answer:
A material which allows current to pass through it is known as a conductor. No conductor will be perfect. It will have some resistance. The property to hinder the flow of current is called resistance and a device which does that is known as a resistor.
When charge is under motion current is produced. Here conductor connected to a potential difference will cause electrons to flow. Now rate of flow of these electrons is considered as magnitude of current which will be ‘i’
Let us assume total number of electrons flowing per unit volume be ‘n’
Charge of an electron be ‘e’ neglecting negative sign as we need only magnitude
Magnitude of total electron charge would be
$\eqalign{
  & q = nV \cr
  & \Rightarrow q = e\left( {nAx} \right) \cr
  & \Rightarrow \dfrac{{dq}}{{dt}} = \dfrac{{de\left( {nAx} \right)}}{{dt}} \cr
  & \Rightarrow \dfrac{{dq}}{{dt}} = Ane\dfrac{{dx}}{{dt}} \cr
  & \therefore i = vAne \cr} $
Where ‘V’ is volume which will be the product of area(A) and displacement(x). cross section area ‘A’ is constant but displacement ‘x’ is varying. Rate of change of displacement is called drift velocity(v).

Note: If charge is given as a function of time then we should differentiate that charge function with respect to time to get current and if current is given as a function of time then we can integrate with respect to time to find charge. We can also find average value of current and r.m.s value of current with that current function