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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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Related Articles and references
- 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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