Question: The dimensions of RC is: [PMT/NEET-1995]
a. square of time
b. square of inverse time
c. time
d. inverse time

Solution
For an RC circuit, the time constant $\tau = RC$.

• Resistance $R = \dfrac{V}{I} $.
  Using Ohm’s law: $V = Work/Charge = \dfrac{ML^{2}T^{-2}}{AT} = ML^{2}T^{-3}A^{-1}$.
  So,
  $
  R = \frac{V}{I} = \frac{ML^{2}T^{-3}A^{-1}}{A} = ML^{2}T^{-3}A^{-2}
  $

Capacitance $C = \dfrac{Q}{V} = \dfrac{AT}{ML^{2}T^{-3}A^{-1}} = M^{-1}L^{-2}T^{4}A^{2}$.

Now,
$
RC = (ML^{2}T^{-3}A^{-2})(M^{-1}L^{-2}T^{4}A^{2}) = T
$

Answer
c. time