Question

Find the dimensional formula of
(a) coefficient of viscosity `eta` (b)charge `q`
(c ) potention `V` (d) capacitance `C` and
( e) resistance `R`
Some of the equations containing these quantities are
`F= -etaA [[Deltau )/(Delta ]], q = It. U = VIt, q = CV and V = IR `
where A denotes the v the velocity , I is the length ,I the electric current, t the time and U the energy .

Answer 1

(a)` eta = -(F)/(a) (Delta l)/(Delta u) rArr :.[eta] = ([F][I])/([A][v]) = ([MLT^(-2)][L])/([L^(2)][LT^(-1)]) = [ML^(-1) T^(-1)]`
(b)` q= it rArr :. [q]= [I][t] = ,AT]`
(c ) `U= Vit`
`V = (U)/(it) or [V] = ([U])/([I][t]) = ([MLT^(-2)T^(-2)])/([A][T]) = [MLT^(2)T^(-1)]`
(d) `q= CV`
` :. C= (q)/(v) ` or `[C] = ([q])/([v]) = ([AT])/([MLT^(2)T^(-3) A^(-1)]) = [M^(-1)L^(-3) T^(4)A^(2)]`
(e) ` V = IR`
`:. R= (V)/(T) or [R ] = ([V])/([I]) = ([ML^(2)T^(-3)A^(-1)])/([A])=[ML^(3)T^(-3)A^(-2)]`