## Saturday, November 20, 2010

### Mutual Inductance and Transformers

Transformers make use of mutual inductance. In this process the changing magnetic field produced by the "primary" coil induces electric potential in the "secondary" coil. The primary coil is the one attached to an alternating current power source. An alternating current ("AC") increases then decreases in one direction then reverses, increasing then decreasing in that direction. The changing current creates a changing magnetic field. The changing magnetic field induces electric potential in the nearby secondary coil, which is attached to a load.
Transformers consist of stationary solid core coils near one another.
Every one who lives in a developed country depends on transformers. Transformers "step down" high voltage power delivered from hydro dams or other far away generators to 240 V delivered to the house. Other devices such as televisions and computer monitors use transformers to step up voltage from the 120 V wall outlets supply to the 2500 V needed by CRT's (television tubes).

Whether the voltage is stepped up or down and by how much depends on the relative number of turns on the two coils. The basis of this wizardry is the Law of Conservation of Energy. Power in an electric circuit is directly proportional to current and voltage:
P = IV .
Ideally the power developed in the secondary coil would be the same as developed in the primary:
Pp = Ps .

Ignoring the heat loss that occurs we will take this as an accurate statement: therefore,
IpVp = IsVs.

Rearranging this equality we are able to compare the relative voltages and currents in the primary and secondary coils:
Ip/Is = Vs/Vp .

What this last equality is saying is that you don't get something for nothing. If you use a transformer to double the voltage, you only get half the current. At best, ignoring heat losses, you get the same power from the secondary as delivered to the primary.

As indicated by Faraday's law, the electric potential induced is directly proportional to the number of loops or

turns in the coil. Therefore,
Ns/Np = Vs/Vp = Ip/Is .

In functioning transformers, hundreds or thousands of turns are used. The transformer depicted above has

Np = 4 and Ns = 2. Therefore

Ns/Np = Vs/Vp = 0.5

Therefore, if 120 V was delivered to the primary coil,
0.5 = Vs/(120 V)

the voltage delivered to the load in the secondary coil would be
Vs = 60 V. This would be a step-down transformer.
If the source delivered 2 A of current to the primary coil (Ip = 2 A) then

Ns/Np = Ip/Is and

0.5 = (2 A)/Is and

Is = 4 A .

(At best we get half the voltage; twice the current. Nothing gained; nothing lost.)