Ideal transformer calculation: A transformer has a 300-turn secondary producing 360 Vac. If the primary has 150 turns, what input (primary) voltage is required (assume an ideal transformer)?

Introduction / Context:Transformer voltage ratios follow directly from the turns ratio. Quick mental calculations using V ∝ N allow you to size windings, anticipate secondary voltages, and verify lab measurements, assuming ideal behavior (no losses, perfect coupling).

Given Data / Assumptions:

• Secondary turns N_s = 300 with V_s = 360 Vac.
• Primary turns N_p = 150; find V_p.
• Ideal transformer: V_p / V_s = N_p / N_s.

Concept / Approach:For ideal transformers, the voltage ratio equals the turns ratio: V_p / V_s = N_p / N_s. If the primary has fewer turns than the secondary (N_p < N_s), the primary voltage must be proportionally lower than the secondary voltage for the same flux level.

Step-by-Step Solution:

Verification / Alternative check:Cross-check direction: Secondary has more turns (step-up 2:1 from primary), so for a given secondary of 360 Vac the primary should be half of that—180 Vac. Units and proportions are consistent.

Why Other Options Are Wrong:

• 2.4 Vac: Off by a factor of 75; not consistent with 2:1 ratio.
• 150 Vac: Does not match the exact ratio; would imply N_p/N_s = 150/300 = 0.4167, which is incorrect arithmetic.
• 720 Vac: Would correspond to reversing ratio; not applicable here.

Common Pitfalls:Inverting the ratio or mixing up which side is primary vs secondary; always align V with its corresponding N.

Final Answer:180 Vac