# RLC circuits and frequency

• Engineering
• juanpablod
In summary, the problem at hand involves finding the frequency in cycles per second (angular frequency divided by 2 Pi) of the gradually decaying oscillatory current in an electrical circuit with a Leyden jar of capacitance C=10^-9 farads, a copper wire of self-inductance L=3 x 10^-7 and resistance R=5x10^-3 ohms. The steps to solve this problem include drawing a circuit diagram, writing the differential equation associated with the circuit, and solving it to obtain a decaying sinusoid. There is a direct formula for this, but it can also be derived from first principles using circuital laws.

#### juanpablod

Oscillation frequency

I'm not sure what to do for this question. I have found a few things of relevancy but I'm making the problem more complex than it really is?

A leyden jar of capacitance C=10^-9 farads is short circuited with a copper wire of self-inductance L=3 x 10^-7 and resistance R=5x10^-3 ohms.

find the frequency in cycles per second (angular frequency divided by 2 Pi) of the (gradually decaying) oscillatory current.

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Do i need to use these values in the form ax'' + bx' + cx = f(t). If so what is f(t) meant to represent?

find the number of oscillations per e-folding of the gradual decay. (i.e. in the time that the amplitude reduces from a to a/e).

I'm not sure what this question means, how do the e-foldings relate to this?

Any help is appreciated. I'm fairly sure i could do this question if i knew the relationship. Am i missing the obvious?

Thanks. Pablod

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This is electrical circuit analysis. Here are the steps:

1. Draw a picture of the circuit
2. Write the differential equation associated with the circuit
3. Solve the differential equation - it will be a decaying sinusoid

Have you done any circuit analysis?

juanpablod said:
find the frequency in cycles per second (angular frequency divided by 2 Pi) of the (gradually decaying) oscillatory current.

There is actually a direct formula for this because RLC circuits are common. However, depending on the intention of the exercise, you should or should not be using it. It all can be derived from first principles, that is circuital laws.

Try doing what hotvette has already suggested if you haven't.

## 1. What is an RLC circuit?

An RLC circuit is an electrical circuit that consists of a resistor (R), an inductor (L), and a capacitor (C) connected in series or in parallel. These components work together to create a resonant frequency, which determines the behavior of the circuit.

## 2. What is the resonant frequency of an RLC circuit?

The resonant frequency of an RLC circuit is the frequency at which the impedance of the circuit is at its minimum. This occurs when the reactive components (inductance and capacitance) cancel each other out, leaving only the resistance component.

## 3. How do I calculate the resonant frequency of an RLC circuit?

The resonant frequency of an RLC circuit can be calculated using the formula f0 = 1/2π√(LC), where f0 is the resonant frequency, L is the inductance in henries, and C is the capacitance in farads.

## 4. What is the difference between series and parallel RLC circuits?

In a series RLC circuit, the components are connected one after the other in a single loop. In a parallel RLC circuit, the components are connected side by side, each with its own branch. Series circuits have the same current flowing through all components, while parallel circuits have the same voltage across all components.

## 5. How does frequency affect an RLC circuit?

The frequency of an input signal can greatly impact the behavior of an RLC circuit. At the resonant frequency, the circuit will have maximum current and minimum impedance, making it ideal for certain applications such as filtering. At frequencies above or below the resonant frequency, the impedance of the circuit will increase, affecting its ability to effectively pass or block signals.