Ideal transformer current scaling — A 100 Vac primary draws 500 mA. For a 300 Vac secondary on the same core (ideal assumptions), what secondary current is expected?

Introduction:
In an ideal transformer, power is conserved (neglecting losses). Therefore, voltage and current scale inversely with the turns ratio. This question practices applying the fundamental V–I relationships to predict secondary current from known primary conditions.

Given Data / Assumptions:

• Primary voltage Vp = 100 Vac, primary current Ip = 0.5 A.
• Secondary voltage Vs = 300 Vac.
• Ideal transformer: Vp * Ip ≈ Vs * Is (ignoring losses), same frequency on both sides.

Concept / Approach:

For an ideal transformer, power in equals power out. Hence Is = (Vp * Ip) / Vs. Voltage is stepped up by a factor of 3 (300/100), so current is stepped down by the same factor to conserve power.

Step-by-Step Solution:

Verification / Alternative check:

Using ratios: Vs/Vp = 3, so Is/Ip = Vp/Vs = 1/3 → Is = 0.5/3 = 0.1667 A, confirming 167 mA.

Why Other Options Are Wrong:

• 1500 mA: Would imply an impossible power increase.
• 200 mA / 150 mA / 50 mA: Do not match the exact inverse scaling by 3.

Common Pitfalls:

• Confusing which side is stepped up; higher voltage side carries proportionally lower current.
• Ignoring real transformer losses; they slightly reduce output current for a given load but not to this magnitude.

Final Answer:

167 mA