InterviewSolution
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InterviewSolution
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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 . |
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Answer» (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)]` |
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