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

English

Gujarati

Hindi

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

In a typical combustion engine the work done by a gas molecule is given $W =\alpha^{2} \beta e ^{\frac{-\beta x ^{2}}{ KT }}$, where $x$ is the displacement, $k$ is the Boltzmann constant and $T$ is the temperature. If $\alpha$ and $\beta$ are constants, dimensions of $\alpha$ will be

hard

(JEE MAIN-2021)

If $R$ and $L$ represent respectively resistance and self inductance, which of the following combinations has the dimensions of frequency

medium

An expression for a dimensionless quantity $P$ is given by $P=\frac{\alpha}{\beta} \log _{e}\left(\frac{ kt }{\beta x }\right)$; where $\alpha$ and $\beta$ are constants, $x$ is distance ; $k$ is Boltzmann constant and $t$ is the temperature. Then the dimensions of $\alpha$ will be

medium

(JEE MAIN-2022)

Force $(F)$ and density $(d)$ are related as $F\, = \,\frac{\alpha }{{\beta \, + \,\sqrt d }}$ then dimension of $\alpha $ are

medium

The Martians use force $(F)$, acceleration $(A)$ and time $(T)$ as their fundamental physical quantities. The dimensions of length on Martians system are

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

Similar Questions

In a typical combustion engine the work done by a gas molecule is given $W =\alpha^{2} \beta e ^{\frac{-\beta x ^{2}}{ KT }}$, where $x$ is the displacement, $k$ is the Boltzmann constant and $T$ is the temperature. If $\alpha$ and $\beta$ are constants, dimensions of $\alpha$ will be

If $R$ and $L$ represent respectively resistance and self inductance, which of the following combinations has the dimensions of frequency

An expression for a dimensionless quantity $P$ is given by $P=\frac{\alpha}{\beta} \log _{e}\left(\frac{ kt }{\beta x }\right)$; where $\alpha$ and $\beta$ are constants, $x$ is distance ; $k$ is Boltzmann constant and $t$ is the temperature. Then the dimensions of $\alpha$ will be

Force $(F)$ and density $(d)$ are related as $F\, = \,\frac{\alpha }{{\beta \, + \,\sqrt d }}$ then dimension of $\alpha $ are

The Martians use force $(F)$, acceleration $(A)$ and time $(T)$ as their fundamental physical quantities. The dimensions of length on Martians system are

Start a Free Trial Now