Q125 / 180 · COMEDK 2013 · Physics

The dimensional formula for inductance is

  • Correct answer
    A
    $\left[\mathrm{ML}^{2} \mathrm{T}^{-2} \mathrm{A}^{-2}\right]$
  • B
    $\left[\mathrm{ML}^{2} \mathrm{TA}^{-2}\right]$
  • C
    $\left[\mathrm{ML}^{2} \mathrm{T}^{-1} \mathrm{A}^{-2}\right]$
  • D
    $\left[\mathrm{ML}^{2} \mathrm{T}^{-2} \mathrm{A}^{-1}\right]$

Solution

As we know, magnetic flux, $\phi=L I$ $$ \begin{aligned} &\Rightarrow \quad L=\frac{\phi}{I}=\frac{B A}{I} \\ &\therefore \text { Dimensions of }[\mathrm{L}]=\frac{[\mathrm{B}][\mathrm{A}]}{[\mathrm{I}]} \\ &=\frac{\left[\mathrm{ML}^{0} \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]\left[\mathrm{L}^{2}\right]}{[\mathrm{A}]}=\left[\mathrm{ML}^{2} \mathrm{~T}^{-2} \mathrm{~A}^{-2}\right] \end{aligned} $$

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

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