**Dimensional Formula of Resistance **

**with its Derivation**

In this article, we will find the dimension of Resistance

The dimensional formula for Resistance is

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

Where

M -> Mass

L -> Length

T -> Time

I -> Current

We would now derive this dimensional formula.

### Derivation for expression of Dimension of Resistance

As per Ohm’s Law

$V= IR$

or

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

Now the dimension of Current = $[I^1]$

Lets derive the dimension of Potential ( Voltage)

Now

$V = E \times d$

or

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

Now dimension of Force = $[M^1 L^1T^{-2}]$

Dimension of Charge = $[I^1 T^1]$

So dimension of E = $ \frac {[M^1 L^1T^{-2}]}{ [I^1 T^1]}= [M^1 L^1T^{-3}I^{-1}]$

Now Dimension of Voltage = $ [M^1 L^1T^{-3}I^{-1}] \times [L]= [M^1 L^2T^{-3}I^{-1}]$

Hence Dimension of Resistance is given by

$= \frac {[M^1 L^2T^{-3}I^{-1}]}{[I^1]} = [M^1 L^2T^{-3}I^{-2}]$

Unit of Resistance is Ohm

I hope you this post on dimension of resistance.Please do provide the feedback

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- New Simplified Physics by SL Arora : I highly recommend this book for class 11 Physics students. It is easy to understand with lots of solved problems.
- Dimensional Analysis:- a very good website for physics concepts
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