### Problem StatementAn AC circuit has a 300-Ω resistor in series with a 10-μF capacitor and a 900-mH inductor. What is the resonance frequency of the circuit?### Options- ○ 100.5 Hz- ○ 12.5 MHz- ○ 53.05 Hz- ○ 0.54 kHz- ○ 1.9 MHz### ExplanationThis question requires the calculation of the resonance frequency for an RLC circuit. The resonance frequency \( f_0 \) in a series LC circuit is given by the formula:\[ f_0 = \frac{1}{2\pi\sqrt{LC}} \]Where:- \( L \) is the inductance - \( C \) is the capacitance For this problem:- \( L = 900 \) mH \( = 900 \times 10^{-3} \) H- \( C = 10 \) μF \( = 10 \times 10^{-6} \) FBy substituting these values into the formula, the resonance frequency can be calculated.

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Answered: An ac circuit has a 300- resistor in…

An ac circuit has a 300- resistor in series with a 10-µF capacitor and a 900- mH inductor. What is the resonance frequency of the circuit? 100.5 Hz 12.5 MHz 53.05 Hz 0.54 kHz 1.9 MHz

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

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Question

### Problem Statement

An AC circuit has a 300-Ω resistor in series with a 10-μF capacitor and a 900-mH inductor. What is the resonance frequency of the circuit?

### Options

- ○ 100.5 Hz
- ○ 12.5 MHz
- ○ 53.05 Hz
- ○ 0.54 kHz
- ○ 1.9 MHz

### Explanation

This question requires the calculation of the resonance frequency for an RLC circuit. The resonance frequency \( f_0 \) in a series LC circuit is given by the formula:

\[
f_0 = \frac{1}{2\pi\sqrt{LC}}
\]

Where:
- \( L \) is the inductance
- \( C \) is the capacitance

For this problem:
- \( L = 900 \) mH \( = 900 \times 10^{-3} \) H
- \( C = 10 \) μF \( = 10 \times 10^{-6} \) F

By substituting these values into the formula, the resonance frequency can be calculated.

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