If R and L represent respectively resistance and self-inductance, which of the following combinations has the dimensions of frequency: [PMT/NEET-1996]
a. $ \dfrac{R}{L} $
b. $ \dfrac{L}{R} $
c. $ \sqrt{\dfrac{R}{L}} $
d. $ \sqrt{\dfrac{L}{R}} $

Solution

• Resistance $R = ML^{2}T^{-3}A^{-2}$
• Inductance $L = ML^{2}T^{-2}A^{-2}$

Now,
$
\frac{R}{L} = \frac{ML^{2}T^{-3}A^{-2}}{ML^{2}T^{-2}A^{-2}} = T^{-1}
$

This is the dimension of frequency.

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