The dimensions of coefficient of self inductance are

The dimensions of coefficient of self inductance are
  1. $\left[\mathrm{ML}^{2} \mathrm{~T}^{-2} \mathrm{~A}^{-2}\right]$
  2. $\left[\mathrm{ML}^{2} \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]$
  3. $\left[\mathrm{MLT}^{-2} \mathrm{~A}^{-2}\right]$
  4. $\left[\mathrm{MLT}^{-2} \mathrm{~A}^{-1}\right]$

Solution

Energy stored in an inductor, $U=\frac{1}{2} L I^{2}$ $\Rightarrow \mathrm{L}=\frac{2 \mathrm{U}}{\mathrm{I}^{2}}$
$[\mathrm{L}]=\frac{\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]}{[\mathrm{A}]^{2}}=\left[\mathrm{ML}^{2} \mathrm{~T}^{-2} \mathrm{~A}^{-2}\right]$ undefined

Asked in: JEE Mains - Units and Dimensions - Test 1

Practice more Units and Dimensions questions on Aicharya