Question

dimensional formula of inductance

Answer 1

[ML[tex]L^2 $T^-2 A^-2$[/tex]]

Answer 2

Inductance :  L : of a coil :  units are  H :  Henry  in SI system
  we get the dimensions as follows:

 voltage across an inductor is the product of inductance and change of rate of current through it.
                  V =  - L d I/dt 
              V I  = power  = Energy /sec
                   I = ampere = [ A ]
                =>  Volt V = [ M ] [ L² ] [ T⁻³ ] [ A⁻¹ ]
                 L =  [ V ] [ T ] / [ A ]
          
       So L = [ M  ] [ L² ] [T⁻² ]  [ A⁻² ]

We can also find the dimensions from :  energy stored in an inductor
       = U = 1/2 L A²