Which is the dimensional formula for conductance from the...

Which is the dimensional formula for conductance from the give below? (A) $\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-3} \mathrm{~A}^{2}$ (B) $\mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^{3} \mathrm{~A}^{2}$ (C) $\mathrm{M}^{1} \mathrm{~L}^{-3} \mathrm{~T}^{-3} \mathrm{~A}^{-2}$ (D) $\mathrm{M}^{1} \mathrm{~L}^{-3} \mathrm{~T}^{3} \mathrm{~A}^{2}$

Which is the dimensional formula for conductance from the give below?
(A) $\mathrm{M}^{1} \mathrm{~L}^{2} \mathrm{~T}^{-3} \mathrm{~A}^{2}$
(B) $\mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^{3} \mathrm{~A}^{2}$
(C) $\mathrm{M}^{1} \mathrm{~L}^{-3} \mathrm{~T}^{-3} \mathrm{~A}^{-2}$
(D) $\mathrm{M}^{1} \mathrm{~L}^{-3} \mathrm{~T}^{3} \mathrm{~A}^{2}$

Key Concepts

Dimensional Analysis

Dimensional analysis is a method used to express any physical quantity in terms of fundamental base units such as mass (M), length (L), time (T), and electric current (A). This technique allows one to verify the consistency of equations, derive relations between different physical quantities, and compare physical dimensions independent of the specific units used in measurements.

Dimensional Formula

A dimensional formula expresses a physical quantity using the base quantities raised to appropriate powers. It provides insight into the relationship between the quantity in question and the fundamental dimensions, helping identify how different units interact in physical equations.

Electric Conductance

Electric conductance is a measure of how easily electric current flows through a material or component. It is defined as the reciprocal of electrical resistance. In dimensional terms, understanding the conductance involves knowing the dimensions of resistance and then inverting them to reveal the conductance’ dimensional characteristics.

Reciprocal Relationship in Physics

The concept of reciprocal relationships is common in physics, where one quantity is defined as the inverse of another. In the context of conductance and resistance, establishing the conductance dimensions requires taking the reciprocal of the resistance dimensions, thereby inverting each of the fundamental units' exponents.

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