Draw the resistivity versus temperature $(\rho \to T)$ graph for metals, alloys, and semiconductors.
(N/A) $1$. For metals: The resistivity $\rho_T$ at temperature $T$ is given by $\rho_T = \rho_0 [1 + \alpha(T - T_0)]$. For a limited range of temperatures, this graph is a straight line. At very low temperatures, the graph deviates from linearity and shows a non-linear behavior as shown in the provided figure for copper.
$2$. For alloys: Alloys like nichrome, manganin, and constantan have a very high resistivity compared to pure metals. Their resistivity shows a very weak dependence on temperature, resulting in a nearly flat, slightly increasing straight-line graph.
$3$. For semiconductors: The resistivity of semiconductors decreases exponentially with an increase in temperature. The relation is given by $\rho_T = \rho_0 e^{E_g / k_B T}$, where $E_g$ is the band gap energy. The graph is a downward-sloping curve.
$2$. For alloys: Alloys like nichrome, manganin, and constantan have a very high resistivity compared to pure metals. Their resistivity shows a very weak dependence on temperature, resulting in a nearly flat, slightly increasing straight-line graph.
$3$. For semiconductors: The resistivity of semiconductors decreases exponentially with an increase in temperature. The relation is given by $\rho_T = \rho_0 e^{E_g / k_B T}$, where $E_g$ is the band gap energy. The graph is a downward-sloping curve.
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View SolutionConsider a block of conducting material of resistivity $\rho$ shown in the figure. Current $I$ enters at $A$ and leaves from $D$. We apply the superposition principle to find the voltage $\Delta V$ developed between $B$ and $C$. The calculation is done in the following steps:
$(i)$ Take current $I$ entering from $A$ and assume it to spread over a hemispherical surface in the block.
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$(iii)$ From the $r$ dependence of $E(r)$,obtain the potential $V(r)$ at $r$.
$(iv)$ Repeat $(i)$,$(ii)$ and $(iii)$ for current $I$ leaving $D$ and superpose results for $A$ and $D$.
For current entering at $A$,the electric field at a distance $r$ from $A$ is
$(i)$ Take current $I$ entering from $A$ and assume it to spread over a hemispherical surface in the block.
$(ii)$ Calculate field $E(r)$ at distance $r$ from $A$ by using Ohm's law $E = \rho j$,where $j$ is the current per unit area at $r$.
$(iii)$ From the $r$ dependence of $E(r)$,obtain the potential $V(r)$ at $r$.
$(iv)$ Repeat $(i)$,$(ii)$ and $(iii)$ for current $I$ leaving $D$ and superpose results for $A$ and $D$.
For current entering at $A$,the electric field at a distance $r$ from $A$ is
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View Solution$A$ wire has a resistance of $10\, \Omega$. If its length is increased by $10\%$ by stretching,what will be the new resistance of the wire in $\Omega$?
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