Question

The SI unit of $\dfrac{1}{{2\pi \sqrt {LC} }}$ is equivalent to that of:
(A) Time period
(B) Frequency
(C) Wavelength
(D) Wave number

Answer 1

Hint There are two ways you can solve this question:
First: Like if you observe the expression keenly you will find this is a formula of some quantity.
Second: Find the dimensions of the given expression and then compare it with given answers. Thus you can solve the question.

Complete step by step answer:
As you read the given expression is a formula, yes it is. It is the formula of frequency of alternating EMF. From the chapter alternating current.
Second method is lay man’s method. Proceed like we do,
$\dfrac{1}{{2\pi \sqrt {LC} }}$
Where:
$L$ is inductance
$C$ is capacitance
$2\pi$ has no unit
We know that $\omega L$ and $\dfrac{1}{{\omega C}}$ represents inductance.
Thus $\omega L \times \omega C$ will have no dimensions
Now required expression is $\sqrt {LC}$ or $\sqrt {\dfrac{{{\omega ^2}LC}}{{{\omega ^2}}}}$
So $\sqrt {\dfrac{{{\omega ^2}LC}}{{{\omega ^2}}}}$ will have the dimension of $\sqrt {\dfrac{1}{{{\omega ^2}}}} = \dfrac{1}{\omega }$
And $f = \dfrac{\omega }{{2\pi }}$ , also $2\pi$ has no dimensions

therefore, Option B is correct.

Note An alternating current is one whose magnitude changes sinusoidal with time.
The EMF or voltage whose magnitude changes sinusoidal with time is known as alternating emf and is represented by: $V = {V_o}\sin (\omega t + \theta )$
Where ${V_o}$ is the peak value of alternating current.