ihateblackbox said:
Listen sir, firstly, I didn't mean to offend you so I am sorry if I did.
The problem I have is that although I have understood the equations, I don't really understand the theory behind them.
Its a bit like I know 1+1=2 but I don't know why its so. So I take a different approach, break down what really happens until I understand it.
OK. I didn't mean to sound terse, just emphatic. If you understand conservation of energy and thus power in = power out, and if you understand power = current times voltage then we can talk about how a transformer does what it does...
Around any flowing current is generated a magnetic field. Magnetic fields have energy proportional to the square of the field strength added up over the volume. This means a few things. One it means magnetic fields tend to spread out in order to minimize energy. It also means you can get more energy per current by concentrating the B field. This occurs when we loop the wire in a coil.
The relationship between the energy of the B field around a coil of wire and the current through the wire is its
self inductance. It has an analogous relationship to mass for a moving object (current being moving charge). We see this in the analog equations:
Kinetic energy is 1/2 mass times velocity squared,
Magnetic energy is 1/2 inductance times current squared.
So if you have a coil of wire and you at one instant start to apply a voltage the current will begin to grow. The voltage is pushing the current through the wire. But there is also that power = voltage times current. That energy must go somewhere. With a resistor it goes into heat but if there is no resistance then all that energy will go into an ever growing magnetic field. It is analogous to a top spinning faster and faster as a constant torque is applied.
Now you are applying a voltage to the ends of the looped wire so the voltage must change from one value to the other as you measure it along the length of the wire. What happens is that the growing B field around the wire will cause a back reaction, an induced voltage in the wire opposing your applied voltage.
In the mechanical analogue imagine pushing a train (on a frictionless rail system). The whole train will accelerate together but each car feels only one part of the whole force you apply. The inertia of each car "pushes back" so that your whole force is spread out along each car. Just so the growing B field pushes back on the current in the wire.
Suppose you apply a voltage for a time and the B field grows and then you remove the voltage? We can't just disconnect the voltage source as that will stop the current too. The energy stored in the B field cannot just disappear. What happens in real situations is that your attempt to disconnect doesn't work instantly, instead the "momentum" of the current keeps the charge flowing and it arcs through the air (at high resistance) causing the energy to be dissipated as heat in the spark.
To avoid sparking but to reduce the current and B field back down to zero you can apply a reversed voltage for a time. The fact that the current flows against the voltage means negative work is done on the coil and rather the coil does work on the voltage source. If that is a battery it acts to recharge it.
Now let's see what happens if you put two coils together, let's say in a 1 to 2 ratio. The first coil creates a certain amount of B field for a given current. The 2nd coil will produce twice as much B field and twice as much energy for the same current. But if you put a current of 2I in the first coil and a reverse current of I in the 2nd coil you get a net zero B field.
Now try this. If you build up a current of 2I in the first coil, leaving the 2nd one open so no current flows, then once the field is built up you connect the 2nd coil and disconnect the first here is what will happen. (Again assuming 0 resistance). Instead of a spark the B field is able to keep going by inducing a current of 1I in the 2nd coil. It only needs to be half a great because it has twice the windings. You can then drain off the energy in the B field using the 2nd coil and a reverse voltage.
In this way the double coil system can transfer energy to and from the B field, using either winding. The voltages can be anything you want, higher voltages just speed up the process. Also the currents in both coils can be arbitrary. Their effects add or cancel in so far as the B field is concerned depending on their direction.
But what must be true is that as power goes in the same power goes out. Also what must be true is that the changing B field must have twice the effect on the doubly wound coil in terms of reaction voltage since it is related to half the current and power in = power out.
Putting this all together and doing a bit of calculus with equations for voltage and current gives you a voltage ratio equal to the winding ratio and current ratio reversed and power in = power out.
A very final note is that the above assumes the wires are so very small that all the B field loops through all the turns of both wires with no leakage between windings. This is not the case and a true 2:1 transformer won't quite give you 2:1 voltage and 1:2 current. The magnetic core helps but there is a loss of ratio. In addition resistance causes loss of efficiency (energy goes into heat instead of into B field or out of the secondary).
