A quantity X is given by ϵ 0L(Δ V/Δ t) where, ϵ 0 is the permittivity of free space, L is length, Δ V is potential difference and Δ t is time interval. The dimensional formula for X is the same as that of,

Question

A quantity X is given by ϵ 0L(Δ V/Δ t) where, ϵ 0 is the permittivity of free space, L is length, Δ V is potential difference and Δ t is time interval. The dimensional formula for X is the same as that of, (A) resistance (B) charge (C) voltage (D) current

Tardigrade Admin · Accepted Answer

The dimensional formula for permittivity,

[ϵ_{0}] = M^{- 1} L^{- 3} T^{4} A^{2}

,
dimensional formula for potential difference,

[Δ V] = M L^{2} T^{- 3} A^{- 1}

.
Hence, dimensional formula for

X = ϵ_{0} L \frac{Δ V}{Δ t} = [M^{- 1} L^{- 3} T^{4} A^{2}] [L] \frac{[ M L ^{2} T ^{- 3} A ^{- 1} ]}{[ T ]} = [A]

.

Q. A quantity X is given by ϵ0​LΔtΔV​ where, ϵ0​ is the permittivity of free space, L is length, ΔV is potential difference and Δt is time interval. The dimensional formula for X is the same as that of,

resistance

charge

voltage

current

The dimensional formula for permittivity, [ϵ0​]=M−1L−3T4A2 , dimensional formula for potential difference, [ΔV]=ML2T−3A−1 . Hence, dimensional formula for X=ϵ0​LΔtΔV​=[M−1L−3T4A2][L][T][ML2T−3A−1]​=[A] .

Q. A quantity $X$ is given by $ϵ_{0} L \frac{Δ V}{Δ t}$ where, $ϵ_{0}$ is the permittivity of free space, $L$ is length, $Δ V$ is potential difference and $Δ t$ is time interval. The dimensional formula for $X$ is the same as that of,