{"id":5639,"date":"2019-11-02T23:45:52","date_gmt":"2019-11-02T18:15:52","guid":{"rendered":"https:\/\/physicscatalyst.com\/article\/?p=5639"},"modified":"2022-11-04T12:06:29","modified_gmt":"2022-11-04T06:36:29","slug":"dimension-of-resistance","status":"publish","type":"post","link":"https:\/\/physicscatalyst.com\/article\/dimension-of-resistance\/","title":{"rendered":"What is the dimension of Resistance"},"content":{"rendered":"\n

Dimensional Formula of Resistance <\/strong><\/span><\/h2>\n\n\n\n

with its Derivation<\/strong><\/span><\/p>\n\n\n\n

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.<\/p>\n\n\n\n

Derivation for expression of Dimension of Resistance<\/h3>\n\n\n\n

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<\/p>\n\n\n\n

I hope you this post on dimension of resistance.Please do provide the feedback<\/p>\n\n\n\n

Try the free Quiz given below to check your knowledge of Dimension Analysis:-<\/p>\n\n\n\n

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Quiz on Dimensional Analysis<\/strong><\/span><\/h4>\n
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