Question

L, C and R represent inductance, capacitance and resistance respectively. Which of the following have dimensions of frequency ?

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

Answer 1

The correct option is B $\frac{1}{\sqrt{LC}}$

B

Resonance occur in a series circuit wen the supply frequency causes the voltages across L and C to be equal and opposite in phase. Frequency at which the response amplitude us a relative maximum are known as the system’s resonant frequencies. In a series of resonant circuit, the resonant frequency, $f_r$ can be calculated is

$X_L=X_C$

$2\pi fL=\frac{1}{2\pi fC}$

$f^2=\frac{1}{2\pi L\times 2\pi C}=\frac{1}{4{\pi }^{2}LC}$

$f=\sqrt{\frac{1}{4{\pi }^{2}LC}}$

$f_r=\frac{1}{2\pi \sqrt{LC}}\left(Hz\right)or{\omega }_r=\frac{1}{\sqrt{LC}}\left(rads\right)$