Question

If R,C and L denote resistance, capacitance and inductance. Which of the following will NOT have the dimensions of frequency?

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Using dimensional analysis,we have

$\left[\frac{L}{R}\right]=\left[T\right]\Rightarrow \left[\frac{R}{L}\right]=\left[T^{-1}\right]$

$\left[RC\right]=\left[T\right]\Rightarrow \left[\frac{1}{RC}\right]=\left[T^{-1}\right]$

$\left[\frac{1}{\sqrt{LC}}\right]=\left[T^{-1}\right]$

Only $\left[RCL\right]\ne \left[T^{-1}\right]$