Question

# 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 ${\mathrm{ML}}^{2}{\mathrm{I}}^{-2}{\mathrm{T}}^{-3}$ and ${\mathrm{ML}}^{2}{\mathrm{T}}^{-3}{\mathrm{I}}^{-1}$ 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: $\frac{\left[V\right]}{\left[R\right]}=\frac{\left[{\mathrm{ML}}^{2}{\mathrm{A}}^{-1}{\mathrm{T}}^{-3}\right]}{\left[{\mathrm{ML}}^{2}{\mathrm{A}}^{-2}{\mathrm{T}}^{-3}\right]}=\left[\mathrm{A}\right]$ ⇒ V = IRPhysicsHC Verma - IStandard XI

Suggest Corrections

0

Similar questions
View More

Same exercise questions
View More

People also searched for
View More