Question

In a series RLC circuit, R = 10 $\Omega$, L = 0.1 H, and C = 100 $\mu$F. What is the resonance frequency (in Hz)?

• A. 50.3 Hz
• B. 159.2 Hz
• C. 318.3 Hz
• D. 503.2 Hz

Hint:

Ensure capacitance is in Farads and inductance in Henries for resonance calculations.

Answer 1

The Correct Option is B

Step 1: Recall resonance frequency formula
Resonance frequency ($f$) = $\frac{1}{2\pi \sqrt{L C}}$, where $L$ is inductance, $C$ is capacitance.
Given: $L = 0.1$ H, $C = 100 \mu$F = $100 \times 10^{-6}$ F.
Step 2: Substitute values
$f = \frac{1}{2\pi \sqrt{0.1 \times 100 \times 10^{-6}}}$.
Step 3: Calculate
$\Rightarrow f = \frac{1}{2\pi \sqrt{0.00001}}$.
$\Rightarrow f = \frac{1}{2\pi \times 0.003162} \approx 159.2$ Hz.