Dimensions of resistance in an electrical circuit, in terms...

Dimensions of resistance in an electrical circuit, in terms of dimension of mass $M$, of length $L$, of time $T$ and of current $I$, would be $\quad$ [UP SEE 2007] (a) $\left[\mathrm{ML}^{2} \mathrm{~T}^{-3} \mathrm{I}^{-1}\right]$ (b) $\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]$ [c) $\left[\mathrm{ML}^{2} \mathrm{~T}^{-1} \mathrm{l}^{-1}\right]$ (d) $\left[\mathrm{ML}^{2} \mathrm{~T}-3 \mathrm{I}^{-2}\right]$

Dimensions of resistance in an electrical circuit, in terms of dimension of mass $M$, of length $L$, of time $T$ and of current $I$, would be $\quad$ [UP SEE 2007]
(a) $\left[\mathrm{ML}^{2} \mathrm{~T}^{-3} \mathrm{I}^{-1}\right]$
(b) $\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]$
[c) $\left[\mathrm{ML}^{2} \mathrm{~T}^{-1} \mathrm{l}^{-1}\right]$
(d) $\left[\mathrm{ML}^{2} \mathrm{~T}-3 \mathrm{I}^{-2}\right]$

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Key Concepts

Dimensional Analysis

Dimensional analysis is a method used in physics to express physical quantities in terms of base dimensions like mass, length, time, and current. This technique helps verify the consistency of equations and derive relationships among physical quantities by ensuring that both sides of an equation have equivalent dimensional representations.

Ohm’s Law

Ohm’s Law is a fundamental principle in electrical circuits stating that the voltage across a conductor is directly proportional to the current flowing through it, with resistance as the proportionality constant. This relationship is key to determining the dimensional form of resistance, as analyzing the dimensions of voltage and current leads to understanding the derived units of resistance.

Electrical Resistance

Electrical resistance is a measure of how much a material opposes the flow of electric current. Its dimensions are derived from its relationship with voltage and current as expressed by Ohm’s Law, ultimately yielding a combination of the fundamental dimensions of mass, length, time, and electric current.

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