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What is the dimension of Resistance

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

Try the free Quiz given below to check your knowledge of Dimension Analysis:-


Quiz on Dimensional Analysis


1. A dimensionless quantity

Question 1 of 5

2. Choose the correct statement(s)

Question 2 of 5

3. Which of the following physical quantity as the dimension of \([ML^2T^{-3}]\)

Question 3 of 5

4. Which of the following pair does not have the same dimensions

Question 4 of 5

5. Which of the following is a dimensionless quantity

Question 5 of 5


 


Related Articles and references

  1. 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.
  2. Dimensional Analysis:- a very good website for physics concepts
  3. dimension of Voltage
  4. Dimension of permittivity in Vacuum or free space
  5. Dimensional Formula of Power

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