Which one of the following is dimensionally incorrect?

Options

A. Capacitance `C = [M^(-1)L^(-2)T^(4)A^(2)]`
B. Magnetic field induction B = `[ML^(0)T^(-2)A^(-1)]`
C. Coefficient of self-induction `L = [ML^(2)T^(-2)A^(-1)]`
D. Specific resistance `rho= [ML^(3)T^(-3)A^(-2)]`

Answer

C

Explanation

`[C]= [q^(2)]/([W])= ([AT]^(2))/([ML^(2)T^(-2)])= [M^(-1)L^(-2)T^(4)A^(2)]`
`[B]= ([F])/([I][l])= ([MLT^(-2)])/([A][L])= [ML^(0)T^(-2)A^(-1)]`
`[L]= (epsilon)/((di)/(dt))= ([(W)/(q)][t])/([i])= [(ML^(2)T^(-2))/(AT)]([T])/([A])= [ML^()T^(-2)A^(-2)]`
`[rho]= ([R][A])/([L])= ([ML^(2)T^(-3)A^(-2)][L^(2)])/([L])= [ML^(3)T^(-3)A^(-2)]`
option (c) is dimensionally wrong.