Transformer basics: A transformer's primary is connected to a 60 V AC source, its secondary feeds a 330 Ω load, and the turns ratio is 3:1 (primary:secondary). What is the secondary RMS voltage delivered by the transformer?

Introduction / Context:This problem checks fundamental transformer relations: how the turns ratio links primary voltage to secondary voltage under AC excitation. Correctly interpreting a ratio written as primary:secondary is essential for estimating output levels and sizing loads.

Given Data / Assumptions:

• Primary voltage, Vp = 60 V (AC, RMS).
• Turns ratio Np:Ns = 3:1 (step-down).
• Secondary drives a 330 Ω load; assume ideal transformer and negligible voltage drop inside windings for the voltage calculation.

Concept / Approach:In an ideal transformer, voltage ratio equals turns ratio: Vp / Vs = Np / Ns. Therefore Vs = Vp * (Ns / Np). With a 3:1 step-down, the secondary has one-third the primary voltage.

Step-by-Step Solution:

Verification / Alternative check:If the transformer were ideal, load current would be Is = Vs / RL = 20 / 330 ≈ 0.0606 A, and apparent power on secondary ≈ 1.21 VA. The primary would reflect the same apparent power (neglecting losses), consistent with step-down behavior.

Why Other Options Are Wrong:

• 18 V: Not equal to one-third of 60 V.
• 2 V: Off by a factor of 10; misreading ratio as 30:1.
• 180 V: Would be a step-up, opposite of 3:1 primary:secondary.
• 12 V: Would correspond to a 5:1 step-down from 60 V.

Common Pitfalls:

• Inverting the ratio (treating 3:1 as secondary:primary).
• Mixing peak and RMS quantities; here, all values are RMS.

Final Answer:20 V