In basic transformer theory, a step-down power transformer shows 50 V at its secondary when 150 V is applied at the primary. What is the turns ratio (secondary turns : primary turns) implied by this voltage relationship for an ideal transformer?

Introduction / Context:Transformers relate input (primary) and output (secondary) voltages to the ratio of turns on their windings. This question checks your grasp of the fundamental ideal-transformer relationship between voltage and turns, often used for quick sizing of step-down and step-up designs.

Given Data / Assumptions:

• Primary voltage Vp = 150 V (applied).
• Secondary voltage Vs = 50 V (measured).
• Assume an ideal transformer (no winding resistance, core loss, or leakage).

Concept / Approach:The ideal transformer equation for voltages is Vs / Vp = Ns / Np, where Ns and Np are numbers of secondary and primary turns respectively. Power conservation and magnetizing coupling underpin this relation in the ideal model.

Step-by-Step Solution:

Verification / Alternative check:A step-down by a factor of 3 in voltage (150 V to 50 V) must correspond to one-third as many turns on the secondary as on the primary in the ideal case.

Why Other Options Are Wrong:

Common Pitfalls:Mixing up the order of the ratio (primary:secondary vs secondary:primary) and forgetting to simplify 50/150 to 1/3 are common mistakes.

Final Answer:1/3.