Questions & Answers

Question

Answers

A. Increase

B. Decrease

C. Fluctuate

D. Remain constant

Answer
Verified

$R\propto \dfrac{1}{\tau }$

$R\propto T$

Where $R$ - resistance of metals

$T$ - temperature

$\tau $ - relaxation time

As we know that the resistivity of metal is connected with relaxation time by:

$\rho =\dfrac{m}{n{{e}^{2}}\tau }$

Where $\rho $ - resistivity of metals

$m$ - mass of electron

$e$ - electronic charge

$n$ - electron density

And the relation between resistance and resistivity is:

$\begin{align}

& R=\dfrac{\rho l}{A} \\

& \Rightarrow R=\dfrac{ml}{n{{e}^{2}}\tau A} \\

& \\

\end{align}$

Or we can write as $R\propto T\propto \dfrac{1}{\tau }$

So, when we increase temperature then resistance of the metals will also increase and the relaxation time decreases with increase in temperature.

A time constant appears within the only expression for the transport property of electrical conductivity, which states that the electrical conductivity equals the merchandise of the relief time, the density of conduction electrons, and the square of the electron charge, divided by the electron effective mass in the solid. See Band theory of solids.

Although mostly collision times in metals are quite short (on the order of 10$^{-14}$ s at room temperature), mean free paths range from about 100 atomic distances at room temperature to 106 atomic distances in pure metals near temperature. So the relaxation time will depend upon the metal we choose and then the variation of resistance and temperature.