What is the capacitance and inductance of an ideal wire?

Question

I am reading a magazine for acoustics, one article is about the choice of speaker wire. The article said the ideal speaker wire should has no resistance, capacitance and inductance. I understand that for the low resistance in ideal case but doubts on the capacitance and inductance. We are driving in the speaker with AC signal, says ideal sinusoidal wave, in the text, it is given that the voltage drop on the capacitor which is connected to the AC power should be

$$v_c = I_{max}X_C\sin\omega t $$

where $X_C=1/(\omega C)$. My understanding is for ideal wire, the voltage potential on a short section on the wire should be zero, so we should have $v_c=0$ so does it mean $C\to \infty$ when $\omega\neq 0$?

Similar reasoning but on inductance, we have $$v_L = -I_{max}X_L\sin\omega t $$ so for ideal wire, $X_L$ should be zero. Are those reasoning corret?

Answer 1

This would actually be easier to answer over at the EE stackexchange site since there is a handy schematic editor built in.

First, note that, by speaker wire, we're actually referring to a speaker cable; in this case, a pair of wires.

For each wire, we can assign a series resistance and inductance (per foot), i.e., the $R$ and $L$ of each wire is in series with the load.

Since we do not want a voltage drop from one end of the wire to the other - we want all of the source voltage to appear across the load - the ideal case is that the resistance and inductance is zero, i.e., there is zero voltage drop from one end of the wire to the other.

Now, since we have a pair of wires, we can also define a mutual capacitance (per foot) between the wires. This capacitance appears in parallel with the load. If the capacitance is non-zero, higher frequency currents will be somewhat shunted around the load. So, ideally, the cable capacitance is zero, i.e., there is zero current shunted around the load.

Answer 2

Capacitance approaches infinity when the distance between plates approaches 0. A wire can be thought of as an infinite line of capacitors that have no spacing between them, so the capacitance of each of these capacitors is infinity.

Additionally, the equation for reactance, X, in terms of capacitance C is 1/ωC. We can conclude from this that X approaches 0 as C approaches infinity.