# Let I = Current Through a Conductor, R = Its Resistance and V = Potential Difference Across Its Ends. According to Ohm'S Law, - Physics

Sum

Let I = current through a conductor, R = its resistance and V = potential difference across its ends. According to Ohm's law, product of two of these quantities equals the third. Obtain Ohm's law from dimensional analysis. Dimensional formulae for R and V are ${\text{ML}}^2 \text{I}^{- 2} \text{T}^{- 3}$ and ${\text{ML}}^2 \text{T}^{- 3} \text{I}^{- 1}$ respectively.

#### Solution

Dimensional formula of resistance, [R] = [ML2A−2T−3]    ...(1)
Dimensional formula of potential difference, [V] = [ML2A−1T−3]    ...(2)
Dimensional formula of current,  I = [A]

Dividing (2) by (1), we get:
$\frac{\left[ V \right]}{\left[ R \right]} = \frac{\left[ {ML}^2 A^{- 1} T^{- 3} \right]}{\left[ {ML}^2 A^{- 2} T^{- 3} \right]} = \left[ A \right]$
⇒ V = IR

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#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 1
Chapter 1 Introduction to Physics
Exercise | Q 16 | Page 10
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