Ideal transformer power conservation: An ideal transformer has a 2:1 voltage ratio (primary:secondary) and delivers 100 W at the primary. What is the secondary power output?

Introduction / Context:Understanding how power behaves in an ideal transformer is critical for power supply design and isolation applications. Ideal transformers are lossless: while voltage and current scale with the turns ratio, real power in equals real power out (ignoring negligible magnetizing power in the ideal model).

Given Data / Assumptions:

• Ideal transformer (no copper, core, or stray losses).
• Voltage ratio N_p:N_s = 2:1 (so V_s = V_p/2).
• Primary power P_p = 100 W.

Concept / Approach:For the ideal transformer, P_p = P_s. Voltage and current scale inversely to keep power constant: if the secondary voltage halves (2:1 step-down), the secondary current doubles for the same power transfer. Therefore, regardless of the voltage ratio, the secondary power equals the primary power in the ideal case.

Step-by-Step Solution:

Verification / Alternative check:Let V_p = 200 V, I_p = 0.5 A → P_p = 100 W. With 2:1 step-down, V_s = 100 V. For power conservation, I_s must be 1 A → P_s = 100 W, confirming equality.

Why Other Options Are Wrong:

• 50 W / 75 W / 200 W: These imply losses or gains not present in the ideal model.

Common Pitfalls:Assuming voltage ratio changes power directly; in ideal transformers, current adjusts so power stays constant (ignoring phase considerations with reactive loads).

Final Answer:100 W