Voltage–current trade in an ideal transformer: If the secondary voltage is stepped up by a certain ratio, the secondary current is stepped down by the same ratio (inverse of the turns ratio).

Introduction / Context:
Transformers exchange voltage for current according to their turns ratio. This principle allows transmission at high voltage and low current to reduce I^2R losses, and then stepping down voltage for safe utilization while increasing current. Recognizing the inverse relationship prevents overcurrent conditions and ensures correct component sizing.

Given Data / Assumptions:

• Ideal transformer with turns ratio a = Np/Ns.
• Voltage ratio: Vs/Vp = Ns/Np.
• Current ratio: Is/Ip = Np/Ns (inverse of voltage ratio).

Concept / Approach:
Power conservation in the ideal case implies Vp * Ip = Vs * Is. Combining this with the voltage ratio immediately yields the inverse current ratio. Therefore, if voltage is stepped up by factor k, current is stepped down by factor k, preserving power (neglecting losses).

Step-by-Step Solution:

Verification / Alternative check:
Example: 1:10 step-up. If Vp = 10 V and Ip = 1 A, then Vs = 100 V and Is ≈ 0.1 A (neglecting losses), confirming the inverse relationship.

Why Other Options Are Wrong:
Load power factor and transformer size do not alter the ratio identity; they affect real vs. reactive power and efficiency but not the ideal ratio relationships.

Common Pitfalls:
Confusing primary vs. secondary labels or using the turns ratio directly for current rather than its reciprocal.

Final Answer:
Correct