Step-down calculation: A transformer has a 110 V primary and a 15:1 turns ratio (primary:secondary). With RL = 120 Ω, what is the approximate load voltage?

Introduction / Context:
Here we apply the turns ratio to obtain the secondary voltage of a step-down transformer under load. For most practical cases with modest current and low winding resistance, the ideal ratio gives a good approximation of the load voltage.

Given Data / Assumptions:

• Vp = 110 V (RMS).
• Turns ratio Np:Ns = 15:1.
• Load RL = 120 Ω; assume ideal transformer behavior for voltage estimation.

Concept / Approach:
For an ideal transformer, Vs = Vp * (Ns / Np). A 15:1 primary:secondary ratio means one-fifteenth of the primary voltage appears on the secondary winding.

Step-by-Step Solution:

Verification / Alternative check:
Secondary current would be Is ≈ Vs / RL ≈ 7.33 / 120 ≈ 61 mA. Reflected to primary, Ip ≈ Is / 15 ≈ 4.1 mA; apparent power ≈ 0.45 VA—small, justifying negligible regulation for this estimate.

Why Other Options Are Wrong:

• 73 V: Off by a factor of 10.
• 88 V and 880 V: Do not follow the 15:1 step-down relation.
• 11 V: Would correspond to 10:1, not 15:1.

Common Pitfalls:

• Mistaking 15:1 as secondary:primary, which would predict a step-up.
• Using peak instead of RMS values.

Final Answer:
7.3 V