Regarding the units involved in the relationship \({\rm{τ = RC}}\) , verify that the units of resistance times capacitance are time, that is, \({\rm{\Omega \bullet F = s}}\).

The amount of charge stored on a conductor per unit change in potential difference is known as the capacitance of the conductor.

If the unit of resistance, ohm, is given as volts per Ampere, we have

\(\begin{aligned}{}\Omega &= \frac{{\rm{V}}}{{\rm{A}}}\\ &= \frac{{\rm{J}}}{{\rm{C}}}{\rm{ \times }}\frac{{\rm{s}}}{{\rm{C}}}\\ &= \frac{{{\rm{kg}}{{\rm{m}}^{\rm{2}}}{{\rm{s}}^{{\rm{ - 2}}}}{\rm{ \times s}}}}{{{{\rm{C}}^{\rm{2}}}}}\end{aligned}\)

Thus, we get

\(\Omega = \frac{{{\rm{kg}}{{\rm{m}}^{\rm{2}}}{{\rm{s}}^{{\rm{ - 1}}}}}}{{{{\rm{C}}^{\rm{2}}}}}\)

The units of capacitance \(\left( c \right)\) is shown as coulombs per volts, which is:

\(\begin{aligned}{}c &= \frac{{\rm{C}}}{{\rm{V}}}\\F &= \frac{{\rm{C}}}{{{\raise0.7ex\hbox{${\rm{J}}$} \!\mathord{\left/ {\vphantom {{\rm{J}} {\rm{C}}}}\right.\\} \!\lower0.7ex\hbox{${\rm{C}}$}}}}\\ &= {\rm{C \times }}\frac{{\rm{C}}}{{\rm{J}}}\\ &= \frac{{{{\rm{C}}^{\rm{2}}}{{\rm{s}}^{\rm{2}}}}}{{{\rm{kg}}{{\rm{m}}^{\rm{2}}}}}\end{aligned}\)

The product\({\rm{Rc}}\)is then evaluated as:

\(\begin{aligned}{}T &= Rc\\{\rm{\Omega \times F}} &= \frac{{{\rm{kg}}{{\rm{m}}^{\rm{2}}}{{\rm{s}}^{{\rm{ - 1}}}}}}{{{{\rm{C}}^{\rm{2}}}}}{\rm{ \times }}\frac{{{{\rm{C}}^{\rm{2}}}{{\rm{s}}^{\rm{2}}}}}{{{\rm{kg}}{{\rm{m}}^{\rm{2}}}}}\\{\rm{\Omega \times F}} &= {\rm{s}}\end{aligned}\)

Thus, the required condition is proved.