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# What is the dimension of Resistance

## Dimensional Formula of Resistance

with its Derivation

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:-

#### Quiz on Dimensional Analysis

1. The dimension of torque is

Question 1 of 5

2. Which of the following is a dimensionless quantity

Question 2 of 5

3. A dimensionless quantity

Question 3 of 5

4. Which of the following pair does not have the same dimensions

Question 4 of 5

5. The dimensions of universal gravitational constant are

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