Question

If $y=\frac{t}{{\epsilon }_{0}LV}$ where t is time, $L$ is length, $V$ is potential and ${\epsilon }_0$ is permittivity, then dimension of $y$ is same as that of:

Answer 1

since

$\left[{\epsilon }_0\right]=\left[M^{-1}{L}^{-3}{T}^4{A}^2\right]$

$\left[t\right]=\left[T\right]$

$\left[V\right]=\left[M^1{L}^2{T}^{-3}{A}^{-1}\right]$

$\left[l\right]=\left[L\right]$

from given equation: $y=\frac{t}{{\epsilon }_{0}LV}$

from RHS $\frac{\left[T\right]}{\left[M^{-1}{L}^{-3}{T}^4{A}^2\right]\left[L\right]\left[M^1{L}^2{T}^{-3}{A}^{-1}\right]}$

$=\frac{\left[T\right]}{\left[T^{4-3}{A}^{2-1}\right]}=\frac{\left[T\right]}{\left[T\right]\left[A\right]}$

$=\left[A^{-1}\right]$