Question

The dimension of mutual inductance is (Denote dimension of current as A)

• A. $ML^2 T^2 A^{-2}$
• B. $ML^2 T^{-2} A^{-2}$
• C. $ML^{-2} T^2 A^{-2}$
• D. $ML^{-2} T^{-3} A^{-1}$
• E. $ML^{2} T^{-3} A^{-3}$

Answer 1

Answer: (B)

As we know, induced $\operatorname{Emf}=L \times \frac{\Delta I}{\Delta t}$
$\Rightarrow [ L ] =\frac{[\text { Voltage }][ T ]}{[\text { Current }]}=\frac{\left[ ML ^{2} T ^{-3} A ^{-1}\right][ T ]}{[ A ]} $
$=\left[ M L ^{2} T ^{-2} A ^{-2}\right]$
$\therefore $ Dimension of mutual inductance is
$\left[M L^{2} T^{-2} A^{-2}\right]$