{"id":5617,"date":"2019-11-02T22:38:27","date_gmt":"2019-11-02T17:08:27","guid":{"rendered":"https:\/\/physicscatalyst.com\/article\/?p=5617"},"modified":"2022-11-04T12:06:29","modified_gmt":"2022-11-04T06:36:29","slug":"what-is-the-dimension-of-voltage","status":"publish","type":"post","link":"https:\/\/physicscatalyst.com\/article\/what-is-the-dimension-of-voltage\/","title":{"rendered":"What is the dimension of Voltage"},"content":{"rendered":"\n
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Dimensional Formula of Voltage<\/strong><\/span><\/h2>\n\n\n\n

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

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In this article, we will find the dimension of Voltage<\/p>\n\n\n\n

Dimensional formula for Voltage is<\/p>\n\n\n\n

\"dimension<\/figure><\/div>\n\n\n\n

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

M -> Mass<\/p>\n\n\n\n

L -> Length<\/p>\n\n\n\n

T -> Time<\/p>\n\n\n\n

I -> Current<\/p>\n\n\n\n

We would now derive this dimensional formula.<\/p>\n\n\n\n

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

Derivation of Voltage can be done with any formula which contains voltage<\/p>\n\n\n\n

A. Voltage is defined as Work done per unit Charge<\/p>\n\n\n\n

$V= \\frac {W}{q} $<\/p>\n\n\n\n

Now $W = f \\times d$<\/p>\n\n\n\n

Dimension of Force = $[M^1 L^1 T^{-2}]$<\/p>\n\n\n\n

Dimension of distance = $[L^1]$<\/p>\n\n\n\n

So, Dimension of Work done is =$[M^1 L^1 T^{-2}] \\times [L^1]=[M^1 L^2 T^{-2}]$<\/p>\n\n\n\n

Now charge is given as<\/p>\n\n\n\n

$q = I \\times t$<\/p>\n\n\n\n

Hence Dimension of charge is $[I^1 T^1]$<\/p>\n\n\n\n

Now that we know the dimension of work done and charge, dimension of Voltage will be given by<\/p>\n\n\n\n

$=\\frac {[M^1 L^2 T^{-2}]}{ [I^1 T^1]} = [M^1 L^2 T^{-3} I^{-1}]$<\/p>\n\n\n\n

B. Voltage is also defined as<\/p>\n\n\n\n

$V= E \\times d$<\/p>\n\n\n\n

Where E is the electric Field<\/p>\n\n\n\n

Now Electric Field is defined as<\/p>\n\n\n\n

$E= \\frac {F}{q}$<\/p>\n\n\n\n

Dimension of Force= $[M^1 L^1 T^{-2}]$<\/p>\n\n\n\n

Dimension of charge is $[I^1 T^1]$<\/p>\n\n\n\n

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

Hence Dimension of Voltage is given by<\/p>\n\n\n\n

$=[M^1 L^1 T^{-3} I^{-1}] \\times [L^1]=[M^1 L^2 T^{-3} I^{-1}]$<\/p>\n\n\n\n

Unit of Voltage is Volt<\/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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