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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Chapter1: Units, Trigonometry. And Vectors
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### 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.
Transcribed Image Text:### 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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