A resistor, an inductor, and a capacitor are connected in series?

In summary, when a resistor, inductor, and capacitor are connected in series to an AC source operating at resonance frequency, the current is in phase with the voltage and the total voltage across the inductor and capacitor at any instant is zero.
  • #1
accioquote
31
0

Homework Statement



A resistor, inductor, capacitor are connected in series to an AC source. The AC source is operating at the resonance freq. Which are true?
1.The current is in phase with the driving voltage.
2.The peak voltage across the capacitor is greater than the peak voltage across the inductor.
3.The peak voltage across the inductor is greater than the peak voltage across the capacitor.
4.The peak voltage across the resistor is equal to peak voltage across the capacitor.
5.The total voltage across the inductor and the capacitor at any instant is equal to zero.
6.The peak voltage across the resistor is equal to the peak voltage across the inductor.

Homework Equations







The Attempt at a Solution



So the current is in phase with the voltage at resonant frequency.
The total voltage across the inductor and capacitor at any instant is zero.

Would that be all? Or am I missing out on some logic...
 
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  • #2
accioquote said:

Homework Statement



A resistor, inductor, capacitor are connected in series to an AC source. The AC source is operating at the resonance freq. Which are true?
1.The current is in phase with the driving voltage.
2.The peak voltage across the capacitor is greater than the peak voltage across the inductor.
3.The peak voltage across the inductor is greater than the peak voltage across the capacitor.
4.The peak voltage across the resistor is equal to peak voltage across the capacitor.
5.The total voltage across the inductor and the capacitor at any instant is equal to zero.
6.The peak voltage across the resistor is equal to the peak voltage across the inductor.

Homework Equations



The Attempt at a Solution



So the current is in phase with the voltage at resonant frequency.
The total voltage across the inductor and capacitor at any instant is zero.

Would that be all? Or am I missing out on some logic...
That seems right to me .
 

1. What is the purpose of connecting a resistor, an inductor, and a capacitor in series?

The purpose of connecting these components in series is to create a series RLC circuit, which is commonly used in electronic circuits to filter or adjust the frequency of an electrical signal.

2. How does the placement of these components affect the overall circuit?

The placement of these components in series affects the overall impedance (resistance to current flow) of the circuit. The combined impedance of the resistor, inductor, and capacitor can create a complex impedance that varies with frequency.

3. What is the difference between a series RLC circuit and a parallel RLC circuit?

In a series RLC circuit, the components are connected end-to-end, while in a parallel RLC circuit, the components are connected side-by-side. This results in different relationships between the current, voltage, and impedance in the two types of circuits.

4. What are some real-world applications of a series RLC circuit?

A series RLC circuit can be used in a variety of electronic devices, such as radios, televisions, and speakers. It is also commonly used in power supplies and electronic filters for signal processing.

5. How do the values of the resistor, inductor, and capacitor affect the behavior of the circuit?

The values of these components determine the frequency response of the circuit, including the resonant frequency and the bandwidth. A larger resistor value will result in a lower resonant frequency, while a larger inductor value will result in a higher resonant frequency. The capacitor value affects the overall impedance of the circuit and can be used to tune the circuit to a specific frequency.

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