Question

a wire having a length l and cross sectional area a and charge density n. If the drift velocity of charge career is Vd ,then determine the conductivity of the conductor

Answer 1

Solution;

Given length l ,cross section area a,charge density n and drift velocity V_d;

Total charge is given by;

Q=neAl

e is the charge of a single carrier.

Time taken by charge carriers to move accros the length;

t=$\frac{l}{V_d}$

Current flowing in the conductor is,

I=$\frac Qt=\frac{neAl}{\frac{l}{V_d}}=neAV_d$

Voltage across the conductor;

V=IR

Resistance of the conductor is;

R=$\frac VI=\frac{V}{neAV_d}$

But resistivity of a conductor is given by;

$\rho=\frac{RA}{l}=\frac{V}{neAV_d}×\frac Al=\frac{V}{neV_dl}$ Conductivity of the conductor,$\sigma$ is;

$\sigma=\frac{1}{\rho}=\frac{neV_dl}{V}$

n=charge density

e=electron charge

V_d=drift velocity

l=length of conductor

V=voltage across the conductor.