Sinusoidal Voltage

If the flux variation is sinusoidal,

where Φ_max is the peak value of flux, w is angular frequency, and t is time. Equation 1 becomes

[3]

or the induced voltage also is sinusoidal. This voltage has an effective value

[4]

where f is the frequency of the sine wave. Equation 4 is the relation between voltage and flux for sinusoidal voltage.

Sufficient current is drawn by the primary winding to produce the flux required to maintain the winding voltage. The primary induced voltage in an unloaded transformer is just enough lower than the impressed voltage to allow this current to flow into the primary winding. If a load is connected across the secondary terminals, the primary induced voltage decreases further, to allow more current to flow into the winding in order that there may be a load current. Thus the primary of a loaded transformer carries both an exciting current and a load current, but only the load part is transformed into secondary load current.

Primary induced voltage would exactly equal primary impressed voltage if there were no resistance and reactance in the winding. Primary current flowing through the winding causes a voltage drop IR, the product of primary current I and winding resistance R. The winding also presents a reactance X which causes an IX drop. Reactance X is caused by the leakage flux or flux which does not link both primary and secondary windings. There is at least a small percentage of the flux which is not common to both windings. Leakage flux flows in the air spaces adjacent to the windings. Because the primary turns link leakage flux an inductance is thereby introduced into the winding, producing leakage reactance X at the line frequency. The larger the primary current, the greater the leakage flux, and the greater the reactance drop IX. Thus the leakage reactance drop is a series effect, proportional to primary current.