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# What is the dimension of Voltage

## Dimensional Formula of Voltage

with its Derivation

Dimensional formula for Voltage is

Where

M -> Mass

L -> Length

T -> Time

I -> Current

We would now derive this dimensional formula.

### Derivation for expression of Dimension of Voltage

Derivation of Voltage can be done with any formula which contains voltage

A. Voltage is defined as Work done per unit Charge

$V= \frac {W}{q}$

Now $W = f \times d$

Dimension of Force = $[M^1 L^1 T^{-2}]$

Dimension of distance = $[L^1]$

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

Now charge is given as

$q = I \times t$

Hence Dimension of charge is $[I^1 T^1]$

Now that we know the dimension of work done and charge, dimension of Voltage will be given by

$=\frac {[M^1 L^2 T^{-2}]}{ [I^1 T^1]} = [M^1 L^2 T^{-3} I^{-1}]$

B. Voltage is also defined as

$V= E \times d$

Where E is the electric Field

Now Electric Field is defined as

$E= \frac {F}{q}$

Dimension of Force= $[M^1 L^1 T^{-2}]$

Dimension of charge is $[I^1 T^1]$

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

Hence Dimension of Voltage is given by

$=[M^1 L^1 T^{-3} I^{-1}] \times [L^1]=[M^1 L^2 T^{-3} I^{-1}]$

Unit of Voltage is Volt

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

#### Quiz on Dimensional Analysis

1. A unitless quantity

Question 1 of 5

2. Which of the following has the dimensions of pressure?

Question 2 of 5

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

Question 3 of 5

4. Choose the correct statement(s)

Question 4 of 5

5. The dimension of angular velocity is

Question 5 of 5

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