Question

A quantity $X$ is given by $X$ $={ϵ}_{0}L\frac{\Delta V}{\Delta t}$, where ${ϵ}_0$ is the permittivity of free space, $L$ is a length, $V$ is a potential difference and $t$ is time interval. The dimensional formula for $X$ is the same as that of :

• A. resistance
• B. charge
• C. voltage
• D. current

Answer 1

The correct option is D current

$X=E_{0}L\frac{\Delta v}{\Delta t}$
$E_0=M^{-1}{L}^{-3}{I}^2{T}^4$
$L=M^0{L}^1{T}^0$
$\Delta v=M{L}^2{I}^{-1}{T}^{-3}$
$\Delta t=M^0{L}^0{T}^1$
$X=E_{0}L\frac{\Delta v}{\Delta t}=\left(M^{-1}{L}^{-3}{I}^2{T}^4\right)\left(L^1\right)\frac{\left(M{L}^2{I}^{-1}{T}^{-3}\right)}{\left(M^0{L}^0{T}^1\right)}$$=I^1=$ current