Understanding Electric Displacement in Two-Phase Windings

The question asks about the electric displacement of a winding when supplied by a two-phase source. In the context of electrical machines and power systems, "electric displacement" in this context refers to the electrical phase angle difference between the voltages or currents supplied to different windings.

A standard two-phase AC power supply consists of two alternating voltages (or currents) that have the same frequency and amplitude but are displaced from each other by a specific phase angle. This phase difference is crucial for creating a rotating magnetic field in machines like motors.

Phase Relationship in Two-Phase Supply

In a balanced two-phase system, the two phases are typically designed to be electrically displaced by $90^\circ$. This means that when the voltage (or current) in one phase is at its peak, the voltage (or current) in the other phase is at zero, and vice versa, with a specific leading or lagging relationship.

Let the voltage of phase 1 be represented by $V_1(t) = V_m \sin(\omega t)$.

Then, the voltage of phase 2 in a standard two-phase system would be represented by $V_2(t) = V_m \sin(\omega t - 90^\circ)$ or $V_2(t) = V_m \sin(\omega t + 90^\circ)$. The magnitude and frequency are the same, but there is a $90^\circ$ phase shift.

Winding Placement and Electric Displacement

For a two-phase supply to effectively create a rotating magnetic field in a machine, the windings corresponding to the two phases must be placed physically in the machine's stator such that the magnetic fields they produce are also displaced by the same electrical angle as the supply voltages. If the electrical phase displacement of the supply is $90^\circ$, the windings are typically placed $90^\circ$ apart in electrical degrees around the stator.

Therefore, the electric displacement of the winding (meaning the effective phase difference between the windings as seen by the supply) matches the phase displacement of the two-phase supply itself.

Determining the Angle for Two-Phase Supply

Based on the standard definition and practice for two-phase systems used in applications like AC motors, the phase displacement between the two phases is $90^\circ$. Consequently, the windings designed to operate with such a supply will have an electric displacement corresponding to this angle.

Considering the options provided, $90^\circ$ is the characteristic phase difference for a two-phase supply and the associated winding displacement.

Thus, the electric displacement of a winding in a two-phase supply system is $90^\circ$.

Revision Table: Key Concepts

Additional Information: Why $90^\circ$ for Two-Phase?

The $90^\circ$ displacement in a two-phase system is specifically chosen because it allows for the creation of a uniform, rotating magnetic field when applied to appropriately placed windings. If the windings are placed $90^\circ$ apart physically (corresponding to $90^\circ$ electrical displacement), the interaction of the two time-varying magnetic fields, which are also $90^\circ$ out of phase in time due to the supply, results in a magnetic field that rotates at a constant speed and has a constant magnitude. This rotating field is essential for the operation of many AC machines, particularly induction motors.

Although historically some two-phase systems used other angles or were derived from single-phase supplies (like using a capacitor), the standard and most effective two-phase system for creating a rotating field uses a $90^\circ$ phase difference.