j = nqvd
where vd is the drift velocity.
ρ = E/j
This relationship is known as Ohm's law discovered by german physicist Georg Simon Ohm (1787-1854) in 1826.
(B) Resistivity and temperature
ρ(T) = ρ(T0)[ 1 +α(T-T0)]
where, ρ(T) and ρ(T0) are resistivities at temperature T and T0 respectively and α is constant for a given material which also depends on temperature to a small extent. This constant α is known as temperature coefficent of resistivity.
E = ρj
where ρ is a constant independent of E.
E = V/l
If i is the current flowing inside the wire then current density is given by
j = i/A
putting these values in Ohm's law ρ = E/j we get
V = ρi (l/A)
or , V=Ri
which is known as resistance of a given conductor.
R(T) = R(T0)[1 + α(T - T0)]
In this equation. R (T) is the resistance at temperature T and R(T0) is the resistance at temperature T0. The temperature coefficient of resistance α is the same constant that appears in case of resistivity.
In the next post we'll do some worked examples related to this topic