Find the dimensional formulae of the following quantities:
(a) the resistance `R`
(b) the inductance `L`
© the magnetic field `B`
(d) the permeability of free space `mu_(0)`
(e) the magnetic dipole moment `M`
(f) Planck' s constant `h`
some formulae containing these qunatities are
`V=iR, U =(1)/(2)Li^(2), F=Bil,B=(mu_(0)^(i))/(2r),M=iA, E=hv`
where `V`:electric potential, `i`: electric current, `F`: force, `l`:length `r`: radius, `A` area, `E`: energy, `v`: frequency and `U`: energy.

Explanation

(a) `V=iR rArr R=(V)/(i),V=(W)/(q), W: "work", q: "charge"`
`R=(W)/(qi)`
`[R]=(ML^(2)T^(-2))/(AT.A)=M^(2)LT^(-3)A^(-2)`
(b) `U=(1)/(2)Li^(2)rArr=(2U)/(i^(2))`
`[L]=(ML^(2)T^(-2))/(A^(2))=ML^(2)T^(-2)A^(-2)`
(c) `F=BilrArrB=(F)/(il)`
`[B]=(MLT^(-2))/(AL)=MT^(-2)A^(-1)(d) B=(mu_(0)i)/(2r)rArrmu_(0)=(2Br)/(i)`
`[mu_(0)]=(MT^(-2)A^(-1)L)/(A)=MLT^(-2)A^(-2)`
(e) `M=iA`
`[M]=AL^(-2)`
(f) `E=hvrArrh=(E)/(v)`
`[h]=(ML^(2)T^(-2))/(T^(-1))=ML^(2)T^(-1)`