# Confusion about RLC circuits

One thing that occurred to me when thinking about circuits and the waveforms they can produce started to confuse me. If you have a voltage source and two wires that don't connect to each other, do you have an RLC circuit? In other words, since all materials have some resistance and inductance, and all separated conductors have some tiny capacitance (and isolated conductors have self capacitance), are all electrical systems RLC circuits in some way? If so, does that mean a circuit designed to use capacitors and resistors to make square or triangular waves just has more energy go to that?

## 2 Answers

In principle, the answer to the first two questions is yes. An open circuit can be thought as one with an ideally infinite resistance between the open end-point, or a zero capacitance. These values are idealisations that do not really occur in practice. This is why, for instance, a battery that is not connected to anything will degrade over time: in fact, the high voltage end is connected to the low one by a high (but not infinite) resistance, e.g. air.

For your last question, which I have to interpret a bit, I guess the answer is that, by attaching any other electrical component to the open circuit, you are changing the parameters (L, R and C) in some way. A resistor would definitely lower the overall resistance, as this can be thought as in parallel with the "infinite" one (a series is just another open circuit), and so on.

You suggest an LCR-circuit, where, I guess, the 3 elements, the resistor has a rather high resistance, the inductance and the capacitance have small values. This will make an LCR-circuit, but with an oscillating frequency $$f = \frac{1}{2\pi \sqrt{LC}}$$ very high. This means this LCR-circuit will not be excited at the usual frequencies. Which ones, of course depends on the actual values of $L$ and $C$. Anyway, it already happened in many circumstances (typically in laboratories, but also other places) that something started oscillating (I assume here an external excitation) like an LCR-circuit at a typically high frequency nobody had expected before because nobody thought about it earlier that under the given circumstance the relation $$f = \frac{1}{2\pi \sqrt{LC}}$$ could be fulfilled (by the device in question, where $L$ and $C$ were never measured before).

Nevertheless another parameter of an LCR-circuit plays an important role, which is the quality factor $Q$ of an LCR-circuit:

$$Q = \frac{1}{R}\sqrt{\frac{L}{C}} \, .$$

As we assume a high resistance, let's say the inductance and capacitance of similar magnitude, the high resistance will prevail, and the quality factor will be low. The quality factor expresses the damping rate (dimensionless) of the oscillation. If the quality factor is low, the oscillation will fade away very quickly and probably nobody will pay attention to it. This is what mostly will happen to the types of LCR-circuits you suggest. Again, it depends on the values of the 3 parameters $R$, $L$ and $C$. If your wires are very good conductors, then the Q-value will probably rather high, and at the appropiate frequency the wire will swing, if it at GHz (THz) or even higher (or lower, depends) frequency.

Needless to say, it does not depend on the energy of the circuit, it's just a game of $L$, $R$ and $C$.

• The components of a [V]RLC circuit can be connected in various ways. You are assuming R(air) in parallel with C(two wires), but the OP could have envisioned R(wires) in series with C.
– amI
Jan 3 '18 at 22:32
• You really should be explicit that your formula for $Q$ is correct for a series LRC. The formula for a parallel LRC is $Q = R/Z$ where $Z\equiv \sqrt{L/C}$. Jan 4 '18 at 0:04