# why resonance is not considered in RC and RL Circuit

Why resonance is considered in RLC circuit and not in RC or RL Circuit

• ...because there is no resonance in a RC or RL circuit – Curd Jan 17 '18 at 10:29
• Resonance, in all of nature, requires 2 modes of energy storage. These circuits have only 1 mode. – analogsystemsrf Jan 20 '18 at 4:26

## 3 Answers

why resonance is not considered in RC and RL Circuit

There are times when resonance is considered in what appears to be a simple RL circuit. Inductors are notorious at having parasitic capacitance and therefore some circuits (that on the face of it are "simple") must consider it as a problem.

Even a simple resistor has ESL (effective series inductance) and parasitic capacitance and, at a high enough frequency will become a resonant tuned circuit.

Capacitors have ESL and can become very resonant to the point that they become ineffective as decoupling capacitors on circuit boards.

If you are just considering theoretically perfect components connected together and the following equation cannot be used in some form or another: -

$f_{res} = \dfrac{1}{\sqrt{LC}}$

Then that is because L or C are not present and the circuit is not resonant.

However, if you are considering the shape of the complex s-plane then any first order filter has an infinite point of "resonance" called a "pole". It's unclear in your question as to whether you are referring to the complex s-plane but I suspect you aren't.

For resonance to occur, energy needs to flow from one component to another and back.

Resistors (R) can only absorb electrical energy and convert that into heat. Then the electrical energy is "lost" and it cannot be retrieved through the resistor.

Capacitors (C) and Inductors (L) however can store and release electrical energy.

So with an RC and RL circuit the energy "escapes" (as heat) through the resistor.

In an LC or RLC circuit, the energy goes back and forth between the Capacitor and Inductor making resonance possible.

General, for a system to be an oscillator, it needs at least two independent enegery storages.

Only oscillatably systems can have a resonant frequency.

On electronics, this can be achieved by a capcitor and an inductor, which are independent by nature.

As a side note: The fact of at least two independent energy storages is not special to electronics. It is a general rule of phsyics and math. In analogy zu mechanics, a spring mass system behaves in the same manner.

• An oscillator doesn't need to contain two independent energy storage devices. It need only contain 1. – Andy aka Jan 17 '18 at 12:08
• The differential equation of the system needs to be at least of second order to be able to oscillate. For that reason, it needs two. The order of the differential equation is equal to the number of independent energy storages. – Finkman Jan 17 '18 at 12:35
• As a side question to Andy aka: If only energy storage is idependent, from which physical value is it independent? The dependency of energy storages is bijective, meaning that if storage A is independent from B, B is also independent from A. – Finkman Jan 17 '18 at 12:43
• A relaxation oscillator uses only a capacitor to store energy. – Andy aka Jan 17 '18 at 12:45
• Somewhere in this discussion the word linearity should be used. The relaxation oscillator is using a nonlinear element to trigger and oscillate, and would not oscillate with only linear behaviour. This does seem to be a tangential argument from the original question however, which is only considering ideal behaviour of linear circuits. – loudnoises Jan 17 '18 at 13:08