Electrical resistance R of a conductor of length l and area of cross section a is given by R = frac{

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1.Units, Dimensions and Measurement

medium

The electrical resistance $R$ of a conductor of length $l$ and area of cross section $a$ is given by $R = \frac{{\rho l}}{a}$ where $\rho$ is the electrical resistivity. What is the dimensional formula for electrical conductivity $\sigma $ which is reciprocal of resistivity?

A$[M^{-1}\, L^{-3}\, T^3\,A^2]$

B$[M\,L^{-3}\, T^{-3}\,A^2]$

C$[M\,L^3\,T^{-3}\,A^{-2}]$

D$[M^{-2}\,L^3\, T^2A^{-1}]$

(AIEEE-2012)

Solution

$\begin{array}{l}
Dimensional\,fomula\,for\,electrical\\
resistivity,\,\rho = \left[ {M{L^3}{T^{ – 3}}{A^{ – 2}}} \right]\\
Dimensional\,formula\,for\,electrical\\
conductivity,\,\sigma = \frac{1}{\rho }\,is\,\left[ {{M^{ – 1}}{L^{ – 3}}{A^2}} \right]
\end{array}$

Standard 11

Physics

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medium

The electrical resistance $R$ of a conductor of length $l$ and area of cross section $a$ is given by $R = \frac{{\rho l}}{a}$ where $\rho$ is the electrical resistivity. What is the dimensional formula for electrical conductivity $\sigma $ which is reciprocal of resistivity?

Solution

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