Introduction To Transformers

The beauty with AC is, we can easily step up or down the voltage, and in order to do that we use transformers. A transformer is an electric device with two coils placed on a closed loop metallic core.

Suppose we have a transformer with a primary coil having N_p number of turns, and a secondary coil with N_s number of turns. Our transformer uses U_p as primary voltage and it outputs U_s in the secondary coil. We work with the following equation:

Transformers Formulas:

Us / Up = Ns / Np

which is exactly the same as:
Us * Np = Up * Ns

In the same time we have:
Us / Up = Ip / Is

which is, again, exactly the same as:
Us * Is = Up * Ip

Now, because

Up = -Np * dΦ/dt

and
Us = -Ns * dΦ/dt

we can calculate the dimensions of the metallic core. This should be all you need to work successfully with transformers. However, the metallic core manufacturers have Data Sheets specific to their products and you do need to consult them.

Power in AC circuits is: P = I² * Z which may be:

Apparent Power: P_A [VA] = √[P_R² + (P_XL - P_XC)²]

True Power: P_R [W] = P_A * cos(x)

Reactive Power: P_X [VAR] = P_A * sin(x) = P_XL - P_XC

P_A is Apparent Power in [V*A] and you can see in Fig 4 where it comes from; it is the red vector

P_R is True Power in [W] and it is given by pure resistance in AC circuits

P_XC is Reactive Capacitive Power in [V*Ar], and it is lagging PR by (-PI/2)

P_XL is Reactive Inductive Power in [V*Ar]; it is ahead of PR by (+PI/2)

P_X is the difference P_XL-P_XC. It is mandatory that Reactive Inductive Power is greater than Reactive Capacitive Power, due to the issues presented in Design Notes 2

cos(x) is Power Factor (Pf)

VAR is read as "Volt Ampere Reactive" and it is used to mark Inductive and Capacitive reactive currents (only the current is considered as being reactive)

Power factor: P_f = cos(x) = P_R/ P_A = True Power / Apparent Power

NOTE: Because they are opposed by PI (180 degrees, Inductive and Capacitive reactances compensate each other. However, it is better to have slightly inductive AC circuits rather than capacitive ones, because capacitive reactance is very dangerous. Of course too much inductive reactance is not good, and we use capacitors to control it.