Name: Superconductivity: An Overview
Uploaded: 2019-07-19
Duration: 2 min 51 s
Description: Resistance of mercury at very low temperatures reduces to nearly zero. Certain materials exhibit this property of superconductivity. Let's learn more.

Question

Define the term resistivity of a conductor. Give its SI unit. Show that the resistance of a conductor is given by

R = \frac{m l}{n e^{2} τ A}

where the symbols have their usual meanings.

Accepted Answer

Suppose a potential difference V is applied across conduction of length l and of uniform cross-sections A. The electric field E sec up inside the conductor is given by
$E = \frac{V}{l}$
Under the influence of field $\vec{E},$ the free electrons begin to drift in the opposite direction $\vec{E}$ with an average drift velocity $v_{d} .$
Let the number of electrons per unit volume or electron density $= n$
Charge on an electron =e

Number of electrons in length l of the conductor $= n \times$ volume of the conductor $= n A l$
Total charge contained in length l of the conductor is $q = e n A l$ All the electrons which enter the conductor at the right end will pass through the conductor at the left end in time,
$t = \frac{distance}{Velocity} = \frac{l}{v_{d}}$
$∴$ Current, $I = \frac{q}{t} = \frac{e n A l}{l / v_{d}}$
or $I = e n A u_{d}$
This equation relates the current I with the drift velocity $v_{d} .$
The current density $' j'$ is given by
$j = \frac{I}{A} = e n v_{d}$
In vector form $\vec{j} = \frac{I}{A} = e n v_{d}$
The above equation is valid for both positive and negative values of q.
When a potential difference V is applied across a conductor of length l, the drift velocity in terms of V is given by
$v_{d} = \frac{e E τ}{m} = \frac{e V τ}{m l}$ If the area of cross -section of the conductor is A and the number of electrons per unit volume or the electron density of the conductor is n, then the current through the conductor will be
$I = e n A v_{d} = e n A . \frac{e V τ}{m l}$
Or $\frac{V}{I} = \frac{m l}{n e^{2} τ A} .$
At a fixed temperature, the quantities m, l, n, e $τ$ and A, all have constant values for a given conductor.
Therefore,
$\frac{V}{I} =$ R
This proves Ohm’s law for a conductor and where R is the resistance of the conductor.
Hence $R = \frac{m l}{n e^{2} τ A},$

Define the term resistivity of a conductor. Give its SI unit. Show that the resistance of a conductor is given by
$R = \frac{m l}{n e^{2} τ A}$
where the symbols have their usual meanings.

Important Questions on Current Electricity

Learn and Prepare for any exam you want !

Define the term resistivity of a conductor. Give its SI unit. Show that the resistance of a conductor is given by R=mlne2τA where the symbols have their usual meanings.

Important Questions on Current Electricity

Learn and Prepare for any exam you want !

Define the term resistivity of a conductor. Give its SI unit. Show that the resistance of a conductor is given by
$R = \frac{m l}{n e^{2} τ A}$
where the symbols have their usual meanings.