A quantity $X$ is given by $\varepsilon_{0} L \frac{\Delta V}{\Delta t}$ where $\epsilon_{0}$ is the…

A quantity $X$ is given by $\varepsilon_{0} L \frac{\Delta V}{\Delta t}$ where $\epsilon_{0}$ is the permittivity of the 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
  1. resistance
  2. charge
  3. voltage
  4. current

Solution

Dimensionally $\varepsilon_{0} L=$ Capacitance (c)
$\therefore \varepsilon_{0} L \frac{\Delta V}{\Delta t}=\frac{C \Delta V}{\Delta t}=\frac{q}{\Delta t}=I$

Asked in: JEE Mains - Units and Dimensions - Test 2

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