Q112 / 180 · AIIMS 2001 · Physics

Dimension of resistivity is

  • A
    $\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~A}^{-1}$
  • B
    $\mathrm{ML}^3 \mathrm{~T}^{-3} \mathrm{~A}^{-2}$
  • Correct answer
    C
    $\mathrm{ML}^3 \mathrm{~T}^{-2} \mathrm{~A}^{-1}$
  • D
    $\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~A}^{-2}$.

Solution

By definition $$ \begin{aligned} R & =\rho \frac{l}{A} \\ \Rightarrow \quad \rho & =\frac{R A}{l}=\frac{\frac{V}{I} A}{l}=\frac{V A}{I l} \\ \therefore \quad[\rho] & =\frac{[V][A]}{[I][l]} \\ & =\frac{\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~L}^2}{\mathrm{AL}^2}=\left[\mathrm{ML}^3 \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right] \end{aligned} $$

Hence, the correct answer is option: 'C'.

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