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

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

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Quiz on Dimensional Analysis

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1. Choose the correct statement(s)

A dimensionally correct equation may be correct

A dimensionally correct equation may be incorrect

A dimensionally incorrect equation may be correct

A dimensionally incorrect equation may be incorrect

Question 1 of 5

2. The dimensions of universal gravitational constant are

\([ML^{2}T^{-1}]\)

\([M^{-1}L^{3}T^{-2}]\)

\([M^{-2}L^{3}T^{-2}]\)

\([M^{-2}L^{2}T^{-1}]\)

Question 2 of 5

3. The dimension of angular velocity is

\([MLT^{-2}]\)

\([ML^2T^{-2}]\)

\([M^2L^0T^{-1}]\)

\([M^0L^0T^{-1}]\)

Question 3 of 5

4. A unitless quantity

never has nonzero dimensions

does not exist

may have a nonzero dimension

always has nonzero dimensions

Question 4 of 5

5. Which of the following pair does not have similar dimensions

tension and surface tension

angle and strain

Planck's Constant and angular momentum

stress and pressure

Question 5 of 5

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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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