Answer:
It is known that time constant of RC circuit is
\[\tau
=\text{RC}\]
and time constant of LR circuit is
\[\tau
=\text{L}/\text{R}\]
\[\therefore\]
\[\text{RC
=}\frac{L}{R}\]
or
\[\text{C}{{\text{R}}^{\text{2}}}=\text{L}\]
Hence the units of
\[\text{C}{{\text{R}}^{\text{2}}}\]
are those of inductance (L) viz. henry
From
\[e=L\frac{dI}{dt},\,\,\,L=\frac{dt}{dI}\]
\[\therefore\]
Units of L are also
\[\frac{Volt-\,\,\sec
}{ampere}=ohm-\sec\]
.
Again, from
\[E=\frac{1}{2}L{{I}^{2}}\]
,
\[L=\frac{2E}{{{I}^{2}}}\]
Therefore, units of L are also
\[\text{joule}/\text{amper}{{\text{e}}^{\text{2}}}\]
.
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