Ideal transformer calculation: with a primary voltage of 120 V (rms) and secondary voltage of 25 V (rms), if the secondary current is 1 A (rms), what is the primary current (assume an ideal transformer and negligible losses)?

Introduction / Context:Transformers trade voltage for current while conserving apparent power ideally. Being able to move between primary and secondary quantities using ratios is a core skill in power electronics and electrical machines.

Given Data / Assumptions:

• Vp = 120 V rms, Vs = 25 V rms.
• Is = 1 A rms.
• Ideal transformer: input VA equals output VA (neglecting losses).

Concept / Approach:In an ideal transformer, Vp * Ip = Vs * Is. Therefore Ip = (Vs * Is) / Vp. This relation follows from the turn ratio and energy conservation in the magnetic coupling under sinusoidal steady state.

Step-by-Step Solution:Step 1: Write Ip = (Vs * Is) / Vp.Step 2: Substitute values: Ip = (25 * 1) / 120 A.Step 3: Compute Ip = 25 / 120 ≈ 0.2083 A.Step 4: Express in mA: ≈ 208 mA.

Verification / Alternative check:Check ratio consistency: the voltage is stepped down by 120/25 ≈ 4.8, so current should step up by ≈ 4.8. 1 A on secondary corresponds to ≈ 0.208 A on primary, matching the calculation.

Why Other Options Are Wrong:

• 7.8 mA: Too small by a factor of ~27.
• 200 mA or 300 mA: 200 mA is close but not as accurate as 208 mA; 300 mA is too high.
• None of the above: Incorrect because 208 mA is correct.

Common Pitfalls:Forgetting that power (VA) is conserved ideally and incorrectly using turn ratio without considering current inversion leads to errors.

Final Answer:208 mA.