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. Charge
• B. Current
• C. Force
• D. Electric field

Answer 1

The correct option is B Current

The capacitance of a parallel plate capacitor is given by $C=\frac{{\epsilon }_{0}A}{d}$ Hence the dimensions of ${\epsilon }_{0}L$are the same as those of capacitance.
$\therefore Dimensionof{\epsilon }_{0}L\frac{\Delta V}{\Delta t}=\frac{dimensionofC\times dimensionofV}{time}=\frac{dimensionofQ}{time}=\frac{charge}{time}=current(\because Q=CV)$
Hence the correct choice is (B)