# Resonant RLC circuit and in inductance

• Worme
In summary, a resonant RLC circuit can be used as an amplifier for a certain band of frequencies around the resonant frequency. The amplifier should have a gain of 0.5 at 200Hz and 4000Hz. To find the required value of the inductor in Henry, we can use the equation W0=1/(L*C) and write an expression for the ratio of output/input voltage in terms of R, L, and C. With two frequencies and two equations, we can solve for L and C. Additionally, we can consider the equivalent of resistance for alternating currents to find the necessary values.
Worme
1. A resonant RLC circuit can be used as an amplifier for a certain band of frequencies around the resonant frequency. Consider a series RLC circuit as an audio band amplifier with an AC voltage source as the input, and the voltage across the 8.0Ω resistor as the output. The amplifier should have a gain (=output/input ) of 0.5 at 200Hz and 4000Hz . What is the required value of the inductor in Henry?ata

## Homework Equations

3. At resonance Xl=Xc and W0=1/(L*C).
Could you explain me how to do?
Thanks.

Hi W,
Is your problem statement complete ? C isn't mentioneed ?
The section "relevant equations" sure isn't. What have you got that you can use there ?
Make a darwing and post your attempt at solution. Good luck !

Yes C is not mentioneed and so is L. But i know that at resonance a RLC circuit has a frequency 1/(2*pi*sqrt(L*C)). So i know f and R.

No you don't, because you don't know L and C. You only know R.
What you do know: at the two given frequencies ouput/input voltage has to be 0.5. Write down an expression for this ratio in terms of R, L and C. With two frequencies you have two equations with two unknowns. The rest is math.

Ok but what is the relation between frequencies and output/input?

Look under: 2. equations. Oops, empty ! So what do you have in your notes or in your textbook that can help you out here ? It's not that I am playing hide and seek, it's just that I'm not supposed to just hand over the answer, so you'll have to make an effort.

With DC and two resistances it would be easy, right ? Well, what do we have as an equivalent instead of resistance when we are dealing with alternating currents ?

## 1. What is a resonant RLC circuit?

A resonant RLC circuit is an electrical circuit that contains a resistor (R), an inductor (L), and a capacitor (C) connected in series or parallel. This type of circuit exhibits resonance when the inductive reactance and capacitive reactance are equal, resulting in a high amplitude of voltage at a specific frequency.

## 2. How does inductance affect a resonant RLC circuit?

Inductance is the property of a circuit element that causes it to oppose changes in current flow. In a resonant RLC circuit, inductance plays a critical role in determining the resonant frequency and the amplitude of the voltage at that frequency. A higher inductance value will result in a lower resonant frequency and a larger voltage amplitude.

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

In a series resonant RLC circuit, the components are connected in a single loop, with the resistor, inductor, and capacitor in series. This results in a high impedance at the resonant frequency. In a parallel resonant RLC circuit, the components are connected in parallel, and the impedance is at its minimum at the resonant frequency.

## 4. How do you calculate the resonant frequency of an RLC circuit?

The resonant frequency of an RLC circuit can be calculated using the formula: fr = 1/(2π√(LC)), where fr is the resonant frequency, L is the inductance in Henries, and C is the capacitance in Farads.

## 5. What are the applications of resonant RLC circuits?

Resonant RLC circuits have many practical applications, such as in radio and television tuning circuits, bandpass filters, and oscillators. They are also used in electronic equipment to eliminate unwanted frequencies and in power systems to improve power factor and reduce harmonics.

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