Understanding Inductor Behavior in Transformers: Voltage and Current Phasing

[kelvin490]

In an inductor, a current waveform 90^o out of phase with the voltage waveform creates a condition where power is alternately absorbed and returned to the circuit by the inductor. If the inductor is perfect (no wire resistance, no magnetic core losses, etc.), it will dissipate zero power.

I wonder how this will change in the case of transformer. Suppose the primary and secondary coils are of zero resistance and the core is perfectly ferromagnetic, what should be the phase different between the voltage and current in the primary coil? Power is delivered to the secondary circuit so it should not be absorbed by the primary voltage source as in the case of pure inductor.

 

[Hesch]

what should be the phase different between the voltage and current in the primary coil?

There are different models of a transformer. Here is one:

If your transformer is perfect, R_w,p, R_c and R_w,s are zero. Say you load the transformer by a resistor, R_L, the transformer will consume reactive power in X_l,p, X_m and X_l,s. So all in all the transformer will consume the power on the primary side:

S_p = P_L + j( Q_l,p + Q_m + Q_l,s ) = P + jQ

giving a phase shift, φ = arctan( Q / P ). So the phase shift depends on the relation Q/P.

If P→0, then φ→90°.

If P→∞, then φ→0°

If the load is not ohmic, you must add the reactive power consumed by the load, Q_L in the equation above.