# Circuit Resonance

1. Jul 6, 2012

When the frequency of the applied e.m.f. equals the natural frequency of the electrical circuit the current reaches the maximum value and the circuit is said to be in resonance with the in resonance with applied e.m.f.
I am confuse with the natural frequency of the electrical circuit. What is this mean?

2. Jul 6, 2012

### Simon Bridge

The driving frequency at resonance is not the same as the natural frequency - though it is very close to it. The natural frequency is the frequency at which the circuit would oscillate without an oscillating source driving it.

3. Jul 6, 2012

### CWatters

Inductors and capacitors are energy storage devices. If you have a circuit comprising an Inductor and capacitor in series then it's possible for energy to flow back and forth between the capacitor and inductor. It does this most easily at the natural frequency because at the natural frequency the total impedance of the circuit is at a minimium. Therefore at this frequency the losses in the circuit are at a minimium.

You probably know that the impedance of an inductor and a capacitor varies with frequency. For an inductor the impedance increases with frequency. For a capacitor it reduces with frequency. At some frequency the sum of the two impedances is a minium. That's the natural frequency at which the circuit will prefer to resonate.

http://en.wikipedia.org/wiki/RLC_circuit#Natural_frequency

4. Jul 6, 2012

### tiny-tim

are you asking, i] what is the resonant frequency,

or are you asking, ii] what is the difference between the resonant frequency and the natural frequency?​

i] as you know, the impedance of the circuit is different at different frequencies,

and the resonant frequency is the one at which the impedance is real (no reactance)

ii] uart has explained it here …

5. Jul 6, 2012

### DragonPetter

What do you mean by this? That confuses me. I almost want to disagree with you, but there could be something I'm confused about or I might not understand what you mean.

Last edited: Jul 6, 2012
6. Jul 6, 2012

### AlephZero

The first statement is a bit confusing. Let's try a longer version.

The frequency of the (damped) oscillations of a system with no exterrnal forcing depends on the amount of damping. "Natural frequency" usually means the theoretical frequency with zero damping, even though no real systems have zero damping. The change in frequency is very small if the damping is low. The relative frequency change is $\sqrt{1 - \beta^2}$ where $\beta$ is the damping factor, so even if $\beta = 0.2$ the change in frequency is only about 2%. But for high damping levels approaching critical damping the frequency change is NOT small, and if the damping is higher than critical ($\beta > 1$) there are no "oscillations" at all unless there is an external force.

There is also an issue about what you really mean by "at resonance". You can define that as the frequency when the applied force is exactly 90 degrees out of phase with the response. Or you can define it as the frequency where the response is a maximum, for a constant level of force input. The two are not necessarily the same.

For oscillating systems with small amounts of damping, none of this is very important in practice, so people often write as if "natural frequency" = "resonant frequency", rather than being precise about what they mean.

7. Jul 6, 2012

8. Jul 7, 2012

### Simon Bridge

Thanks @AlephZero. I should have said that the resonant frequency is not usually the same as the natural frequency of the circuit.

9. Jul 7, 2012

### tiny-tim

for one LC oscillator, only one frequency (you can check that easily by solving the equations)

(for a complicated circuit with several oscillators, i don't know )

10. Jul 7, 2012

### sophiecentaur

A well designed oscillator circuit will ensure that the basic LC components (or crystal) have high Q, intrinsically) and that the 'coupling' between the resonator and the amplifier / feedback part is very loose. This ensures that the oscillator is affected as little as possible by other influences.
Mechanical clock mechanisms have the same requirement, with the pendulum / balance wheel being as isolated as possible from the source of energy (spring / weights) and the losses in the oscillating bit kept to a minimum (jeweled bearings / pallets etc). A good clock will keep going for many cycles if you remove the drive to it.

When crystals are used in a circuit, they may be driven at overtone frequencies and not at their fundamental - but the oscillation of a bar of quartz is not equivalent to a simple LC combination.