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.
If you have a single tube, the current will flow on it directly without making the $N$ loops. It will result
- a different direction, i.e. different magnetic field,
- its magnetic field will be much weaker.
Having the loops, the magnetic fields created by the induvidual loops is added. Actually, you have "the same current" using $N$ times to produce the field.
If you don't have the loops, you need to multiply the current in the wire, which is in most cases impractical:
- You need to create electronic for higher current (much more costly as to simply looping the wire)
- You need to produce higher voltage
- You need to count with much higher secondary losses, f.e. heat loss.
Best Answer
a fairly nice read....wiki
In short, impedance $X$ is expressed as $$X=X_R+X_I+X_C$$ where the resistive load, $$X_R = R$$, the inductive load, $$X_I=j\omega L$$ the capacitive load, $$X_C=\frac{1}{j \omega C}$$
where, $L,C,R$ are inductance, capacitance and resistance.
Now since you have the complex impedance, find out the $|X|$ to get net impedance in Ohms.
So, to get $L$, we have a formula which as you correctly suspect is dependent on $N$, number of turns.
$$L=\frac{\mu_r \mu_0 N^2A}{l}$$ where, $A$ is circular cross section of solenoid, $l$ is length of solenoid (not of wire), $\mu_0$ permeability of air (a constant) and $\mu_r$ relative permability of core (iron, in your case; probabably; you can find the value here).
you can calculate it here itself.