Answer:
Relaxation time is the time gap between two successive electron collisions in a conductor.
The relationship between the relaxation time (T) and drift velocity (Vd) is given below.
\(v_{d} = \left ( e\frac{E}{m} \right )T\)Where
vd = drift velocity
e = charge of electron
E = field
m = mass of electron
T = Relaxation time
So the expression for relaxation time (T) is
\(T = \left ( v_{d}\frac{m}{e} \right )E\)Let L = Length of the conductor
A = Area of the conductor
n = current density
then current flowing through the conductor is
\(I = -neAv_{d}\) \(I = neA\left ( e\frac{E}{m} \right )T\) \(I = \frac{ne^{2}EA}{m}T\)Feild E can be expressed as
E = V/L
Then current flowing through the conductor becomes
\(I = \frac{ne^{2}VA}{mL}T\) \(\frac{V}{I} = \frac{mL}{ne^{2}TA}\)From ohm’s law
V = IR
R = V/I
\(R = \left ( \frac{m}{ne^{2}T} \right )\frac{L}{A}\) \(R = \rho \frac{L}{A}\)
