Question

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

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

Answer 1

Answer: (D)

$C=\frac{\Delta q}{\Delta V}$
or ${\epsilon }_0\frac{A}{L}=\frac{\Delta q}{\Delta V}$
or ${\epsilon }_0=\frac{(\Delta q)L}{A.\Delta l^{\prime })}$
$X={\epsilon }_{0}L\frac{\Delta V}{\Delta t}=\frac{(\Delta q)L}{A(\Delta V)}L\frac{\Delta V}{\Delta t}$
but $[A]=\left[L^2\right]$
$\therefore X=\frac{\Delta q}{\Delta t}=$ current