Center-tapped secondary — phase relationship of the two half-windings: In a center-tapped transformer, the two secondary end-to-center-tap voltages have equal magnitude and are 180° out of phase with respect to the center tap.

Introduction / Context:Center-tapped secondaries are common in full-wave rectifiers and dual-polarity supplies. The phase between the two half-windings determines how diodes conduct in rectifier circuits and how outputs can be combined to generate positive and negative rails relative to the center tap.

Given Data / Assumptions:

• Ideal transformer with a center-tapped secondary winding.
• The center tap is taken as the reference (0 V).
• Symmetrical construction so both halves have equal turns.

Concept / Approach:Because the two secondary halves are wound in opposite directions relative to the center reference, their instantaneous polarities are opposite. At any instant, one end is at +V with respect to the center tap while the other is at –V of equal magnitude. This phase opposition is 180° when referenced to the center tap, a key requirement for classic full-wave rectifier operation using two diodes and a center tap.

Step-by-Step Solution:

Verification / Alternative check:Oscilloscope traces show two sine waves of equal amplitude mirrored about 0 V when probing each end to the center tap. Dot markings also confirm the opposite instantaneous polarities.

Why Other Options Are Wrong:The relationship does not depend on step-up/down ratio, load, or line frequency, provided symmetry and proper phasing are maintained.

Common Pitfalls:Referencing end-to-end voltage instead of each end to center tap; miswiring that swaps dot orientation causing unexpected phasing.

Final Answer:Correct