Dimensions

We’re given that v2 = u2 + 2axWherev, u = Velocitiesa = Accelerationx = Distance In order for this equation to be correct dimensionally, dimensions of left hand side must be equal to…

We know that Force = mass × accelerationacceleration = velocity/time ⇒ Force = mass × velocity/time Taking dimensions on both sides of this equation[F] = [M] [V]/[T] [F] = [M] [V] [T-1] [F]/[V]…

Dimensional formula of resistance R We know that V = IR ThusR = V/I Taking dimensions on both sides of this equation R = V/I [R] = [V]/[I] [V] = [ML2I-1T-3] [R] =…

Dimensional formula of capacitance C We know that Q = CVWhereQ = ChargeC = CapacitanceV = Voltage Taking dimensions on both sides of formula Q = CV[Q] = [C] [V] [Q] = [IT][V]…

Dimensional formula of potential V We know that U = VItWhereU = EnergyV = PotentialI = Currentt = Time Taking dimensions on both sides of U = VIt [U] = [V] [I] [T]…

Dimensional formula of charge Q We know that Q = ItWhereQ = chargeI = Currentt = time Given formula Q = ItTaking dimensions of quantities on both sides of this equation [Q] =…

Dimension formula of coefficient of viscosity η We know that F = – ηA(v2 – v1)/(x2 – x1)WhereF = ForceA = Areav2 – v1 = Velocity differencex2 – x1 = Distance difference Rearranging…

Dimensional formula of thermal conductivity k We know that Q = k A(θ2 – θ1)t/d WhereQ = Heat energyk = Thermal conductivityθ2 – θ1 = Temperature differenceA = Aread = Thicknesst = Time…

Dimensional formula of surface tension S We know thatS = ρ g r h/2WhereS = Surface Tensionρ = Densityg = acceleration due to gravityr = Radiush = height Writing dimensions of quantities on…