Ideal transformer voltage ratio application: if the turns ratio N1/N2 = 2 and the primary voltage is 120 V (RMS), what RMS voltage appears at the secondary winding?

Introduction / Context:Transformers scale voltages according to their turns ratio. Knowing the primary-to-secondary turns ratio allows quick calculation of the secondary voltage under ideal conditions, assuming negligible losses and magnetizing current effects.

Given Data / Assumptions:

• Turns ratio N1/N2 = 2 (primary has twice as many turns as secondary).
• Primary RMS voltage V1 = 120 V.
• Ideal transformer behavior (V proportional to turns, no load effects considered).

Concept / Approach:For an ideal transformer, V1 / V2 = N1 / N2. Rearranging gives V2 = V1 * (N2 / N1). With N1/N2 = 2, N2/N1 = 1/2, so the secondary voltage is half the primary voltage.

Step-by-Step Solution:Use ratio: V2 = V1 * (N2 / N1).Substitute: V2 = 120 * (1 / 2).Compute: V2 = 60 V.

Verification / Alternative check:Check power consistency for later use: if load draws I2, then ideal I1 = I2 * (N2 / N1) = I2 / 2, preserving apparent power V1 * I1 = V2 * I2 under ideal conditions.

Why Other Options Are Wrong:0 V: implies open-circuit with no induced voltage—incorrect under ideal mutual coupling.36 V or 40 V: do not match the 1/2 ratio.None of the above: incorrect because 60 V is correct.

Common Pitfalls:Inverting the ratio (multiplying instead of dividing); confusing turns ratio with impedance ratio (which uses the square of the ratio).

Final Answer:60 V