# RLC Circuit Calculator

With the RLC circuit calculator, you can **solve any RLC series circuit given its resistance (R), inductance (L), and capacitance (C)**.

This tool can help you:

- Solve any series RLC circuit problems easily;
- Calculate the resonant frequency of an RLC circuit and its bandwidth;
- Obtain the Q-factor of the RLC circuit; and
- Find the damping ratio of an RLC circuit.

All of that without using an RLC circuit formula sheet!

## Calculating the resonant frequency of an RLC circuit

An RLC circuit has three parts:

- A $R$); (
- An inductor (with inductance $L$); and
- A capacitor (with capacitance $C$).

This tool will cover only the simplest configuration: **a series RLC circuit**.

The resonant frequency of an RLC circuit is **the frequency at which the system oscillates with minimum impedance**.

At this frequency, the inductance and capacitance are **equal**, and the system current will be at its **maximum**.

The formula for resonant frequency $f_{0}$ is:

The RLC circuit calculator will automatically find this resonant frequency for you and more!

## Q-factor of an RLC circuit

The RLC circuit calculator can easily find the Q-factor, but what is it?

The **Quality Factor**, or **Q-factor**, gives information about the damping in an oscillating system. We can find the Q-factor of an RLC circuit with the following formula:

Increasing the Q-factor is desirable in many applications since it will indicate that the losses within this system are low.

## Damping ratio of an RLC circuit

The damping ratio (**ζ**) in an RLC circuit describes how the oscillations decay.

Since it is related to $R$ to appear in its formula:

losses, we can expect the resistanceAccording to this value, the system will be:

**Overdamped**if $ζ > 1$;**Underdamped**if $ζ < 1$; or**Critically damped**if $ζ = 1$.

## Example with the RLC circuit calculator

Suppose we have a system with the following parameters:

**R= 30 Ω**;**L = 10 mH**; and**C = 100 μF**.

We can use each of these parameters *separately in each equation* to find the resonant frequency, the Q-factor, and the damping ratio.

**Or we can input them within the RLC circuit calculator all at once** and quickly get what we need without relying on an RLC circuit formula sheet.

After typing in the values, the calculator outputs:

**f₀ = 159.15 Hz**;**Q-factor = 0.3333**; and**ζ = 1.5**.

Which you can check using the respective equations!