Question

Find the dimension formula for resistance.

Answer 1

Step 1: Establish Resistance in terms of Standard Quantities

The formula for Resistance according to Ohm's law is given as,

$R=\frac{V}{I}$

Where, $V$ is the potential difference, and $I$ is the electric current.

The formula for potential difference is,

$V=EL$

Where, $E$ is the electric field, $L$ is the length between the two points in a conductor.

The formula for electric field is,

$E=\frac{F}{q}$

Where, $F$ is force, and $q$ is electric charge.

$\therefore E=\frac{ma}{q}$where $m$ is the mass and $a$ is the acceleration.

$\therefore V=\frac{maL}{q}$

$\therefore R=\frac{maL}{qI}$

Step 2: Evaluate the Dimensional Formula

Substitute the standard units into the above equation to get,

$L=\frac{kg.m{s}^{-2}.m}{As.A}$

$=kg.m^2.s^{-3}.A^{-2}$

$=\left[M{L}^2{T}^{-3}{A}^{-2}\right]$

Hence the dimensional formula for inductance is $\left[M{L}^2{T}^{-3}{A}^{-2}\right]$.