Question

The dimensions of the coefficient of self-inductance are

• A. $\left[M L^{2} T^{- 2} A^{- 2}\right]$
• B. $\left[M L^{2} T^{- 2} A^{- 1}\right]$
• C. $\left[M L T^{- 2} A^{- 2}\right] \, $
• D. $\left[M L T^{- 2} A^{- 1}\right] \, $

Answer 1

Answer: (A)

Energy $U=\frac{1}{2}LI^{2}$
$\Rightarrow \, L=\frac{2 U}{I^{2}}$
$\therefore \left[L\right]=\frac{\left[U\right]}{\left[I\right]^{2}}=\frac{\left[M L^{2} T^{- 2}\right]}{\left[A\right]^{2}}=\left[M L^{2} T^{- 2} A^{- 2}\right]$