Question: Dimension of R is: [PMT/NEET-2003]
a. $ML^{2}T^{-1}$
b. $ML^{2}T^{-3}A^{-2}$
c. $ML^{-1}T^{-2}$
d. None of these

Answer: The correct answer is (b) $ML^2T^{-3}A^{-2}$.

The “R” in this question refers to electrical resistance, a fundamental quantity in electrical circuits.

Dimensional Analysis of Resistance

From Ohm’s Law: $V = IR$

Rearranging: $R = \frac{V}{I}$

Let me find the dimensions step by step:

Voltage (V) dimensions:

• Voltage = Work done per unit charge
• Voltage = $\frac{\text{Energy}}{\text{Charge}} = \frac{[ML^2T^{-2}]}{[AT]} = [ML^2T^{-3}A^{-1}]$

Current (I) dimensions:

• Current = $[A]$

Resistance (R) dimensions:

$R = \frac{V}{I} = \frac{[ML^2T^{-3}A^{-1}]}{[A]} = [ML^2T^{-3}A^{-2}]$