Question

An alternating current is flowing through a series LCR circuit. It is found that the current reaches a value of $1$mA at both $200$Hz and $800$Hz frequency. What is the Resonance frequency of the circuit?

• A. $600$Hz
• B. $300$Hz
• C. $500$Hz
• D. $400$Hz

Answer 1

Answer: (D)

$400$Hz

$\omega L=\frac{1}{\omega C}$ $\omega =\frac{1}{\sqrt{LC}}$
$\Rightarrow X_L$ and $X_C$ will get interchanged.
$\Rightarrow 200L=\frac{1}{800C}\Rightarrow \frac{1}{\sqrt{LC}}=\sqrt{200\times 800}=400$Hz.