Question: Which of the following dimensions will be the same as that of time? [PMT/NEET-1996]
a. $ \dfrac{L}{R} $
b. $ \dfrac{C}{L} $
c. $LC$
d. $ \dfrac{R}{L} $

Solution
We need to compare dimensions with time (T).

• Resistance, $R = ML^{2}T^{-3}A^{-2}$
• Inductance, $L = M L^{2} T^{-2} A^{-2}$
• Capacitance, $C = M^{-1} L^{-2} T^{4} A^{2}$

Now check options:

a. $\dfrac{L}{R} = \dfrac{ML^{2}T^{-2}A^{-2}}{ML^{2}T^{-3}A^{-2}} = T$ ✅

b. $\dfrac{C}{L} = \dfrac{M^{-1}L^{-2}T^{4}A^{2}}{M L^{2} T^{-2} A^{-2}} = M^{-2}L^{-4}T^{6}A^{4}$ (not time)

c. $LC = (ML^{2}T^{-2}A^{-2})(M^{-1}L^{-2}T^{4}A^{2}) = T^{2}$ (square of time)

d. $\dfrac{R}{L} = \dfrac{ML^{2}T^{-3}A^{-2}}{ML^{2}T^{-2}A^{-2}} = T^{-1}$ (inverse time)

Answer
a. $\dfrac{L}{R}$