Question

A quantity $X$ is given by $\varepsilon_{0} L \frac{\Delta V}{\Delta t}$, where $\varepsilon_{0}$ 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 $\varepsilon_{0} \frac{A}{L}=\frac{\Delta q}{\Delta V} $
or $\varepsilon_{0}=\frac{(\Delta q) L}{\left.A . \Delta l^{\prime}\right)}$
$X=\varepsilon_{0} L \frac{\Delta V}{\Delta t}=\frac{(\Delta q) L}{A(\Delta V)} L \frac{\Delta V}{\Delta t}$
but ${[A] } =\left[L^{2}\right] $
$\therefore X =\frac{\Delta q}{\Delta t}=$ current