Question

If m=mass l=length t=time nd i=electric current then dimensionalbformula foe resistence

Answer 1

We know that,

$Resistance(R) = \frac{Voltage(V)}{Current flow (I)}$

Voltage = $\frac{Work done}{Charge}$

⇒ Work done's dimensional formula (S.I. unit = Joule) = $[ML^2T^{-2}]$

⇒ Charge's Dimensional unit = $[IT^{-1}]$

(charge = rate of flow of electric current)

⇒ Voltage = $\frac{Work done}{Charge}$ $= \frac{[ML^2T^{-2}]}{[IT^{-1}]} = [ML^2T^{-3}I^{-1}]$

Current flow(I) = [I]

∴ Dimensional Formula of Resistance = $\frac{Voltage's Dimension}{Current} = \frac{[ML^2T^{-3}I^{-1}]}{I} = [ML^2T^{-3}I^{-2}]$