Question

The symbols L, C, R represent inductance, capacitance and resistance respectively. Dimension of frequency are given by the combination

• A. 1 / RC
• B. R / L
• C. $\frac{1}{\sqrt{LC}}$
• D. C / L

Answer 1

Answer: (A), (B), (C)

The correct options are
A 1 / RC
B R / L
C $\frac{1}{\sqrt{LC}}$

Dimension of impendance is $\Omega$

Dimension of $R$ is $\Omega$

Dimension of $L\omega$ is $\Omega$

Dimension of $\frac{1}{C\omega }$ is $\Omega$

$RC$ has the dimensions of time, so $\frac{1}{RC}$ has dimensions of frequency.

Also, dimensions of $\frac{R}{L}$ is same as that of $w$ i.e. frequency.

Resonant frequency $f_r=\frac{1}{2\pi \sqrt{LC}}$

So, $\frac{1}{\sqrt{LC}}$ also has the dimensions of frequency.