An ac circuit has a 300-2 resistor in series with a 10-μF capacitor and a 900-mH inductor. What is the resonance frequency of the circuit? 100.5 Hz 0.54 kHz 53.05 Hz 1.9 MHz 12.5 MHz
An ac circuit has a 300-2 resistor in series with a 10-μF capacitor and a 900-mH inductor. What is the resonance frequency of the circuit? 100.5 Hz 0.54 kHz 53.05 Hz 1.9 MHz 12.5 MHz
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11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
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![**Question:**
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
- 0.54 kHz
- 53.05 Hz
- 1.9 MHz
- 12.5 MHz
**Explanation:**
The question involves determining the resonance frequency of an RLC circuit where the components are given as follows:
- Resistor (R): 300 Ω
- Capacitor (C): 10 μF (microfarads)
- Inductor (L): 900 mH (millihenrys)
Resonance frequency (\( f_0 \)) in a series RLC circuit is calculated using the formula:
\[ f_0 = \frac{1}{2\pi\sqrt{LC}} \]
Where:
- \( L \) is the inductance in henrys
- \( C \) is the capacitance in farads
This formula will provide you with the frequency at which the circuit will naturally oscillate.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2c067e04-819e-445d-9345-defba0ea4f93%2F0b7afa36-13fd-4189-8a54-4a2050c7d2ff%2Fl9fbhjn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
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
- 0.54 kHz
- 53.05 Hz
- 1.9 MHz
- 12.5 MHz
**Explanation:**
The question involves determining the resonance frequency of an RLC circuit where the components are given as follows:
- Resistor (R): 300 Ω
- Capacitor (C): 10 μF (microfarads)
- Inductor (L): 900 mH (millihenrys)
Resonance frequency (\( f_0 \)) in a series RLC circuit is calculated using the formula:
\[ f_0 = \frac{1}{2\pi\sqrt{LC}} \]
Where:
- \( L \) is the inductance in henrys
- \( C \) is the capacitance in farads
This formula will provide you with the frequency at which the circuit will naturally oscillate.
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