question_answer

Identify the quantity represented by \[CV/\rho \,{{\in }_{0}}\], where C is capacity, V is potential, \[\rho \] is specific resistance and \[{{\in }_{0}}\] is electric permittivity of free space.

Answer:

                As \[C=\frac{{{\in }_{0}}A}{d}\] and \[\rho =\frac{RA}{l}\], where the symbols have their usual meaning, therefore, \[\frac{CV}{\rho {{\in }_{0}}}=\left( \frac{{{\in }_{0}}A}{d} \right)\frac{V}{\left( RA/l \right){{\in }_{0}}}=\frac{V}{R}=I\], the current                                         (\[\because \]\[l\],\[d\] both represent distance) Therefore, the quantity represented is current.