The electrical resistance R of a conductor of | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The electrical resistance is given by $R = \frac{\rho l}{a}$.Rearranging for resistivity,we get $\rho = \frac{R a}{l}$.The dimensional formula for

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) The electrical resistance is given by $R = \frac{\rho l}{a}$.Rearranging for resistivity,we get $\rho = \frac{R a}{l}$.The dimensional formula for resistance $R$ is $[M L^2 T^{-3} A^{-2}]$.The dimensional formula for area $a$ is $[L^2]$.The dimensional formula for length $l$ is $[L]$.Substituting these into the formula for $\rho$:$\rho = \frac{[M L^2 T^{-3} A^{-2}] [L^2]}{[L]} = [M L^3 T^{-3} A^{-2}]$.Electrical conductivity $\sigma$ is the reciprocal of resistivity $\rho$,so $\sigma = \frac{1}{\rho}$.Therefore,the dimensional formula for $\sigma$ is $[M^{-1} L^{-3} T^3 A^2]$.

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 the reciprocal of resistivity?

Similar Questions

In the equation $\frac{dy}{dt} = 2\omega \sin(\omega t + \theta_0)$,what are the dimensions of $(\omega t + \theta_0)$?

The physical quantities not having the same dimensions are:

The $SI$ unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be ..............

The force of interaction between two atoms is given by $F = \alpha \beta \exp \left( - \frac{x^2}{\alpha kt} \right)$,where $x$ is the distance,$k$ is the Boltzmann constant,$T$ is temperature,and $\alpha$ and $\beta$ are two constants. The dimension of $\beta$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module