Transformer calculation: a step-up transformer has a turns ratio of 1:4. If the primary is 115 V (rms), what is the secondary peak voltage?

Introduction / Context:Power transformer problems often require two conversions: turns ratio scaling and rms-to-peak conversion. This question integrates both steps for a step-up transformer, from a 115 V rms primary to the secondary peak value.

Given Data / Assumptions:

• Turns ratio Np:Ns = 1:4 (step-up).
• Primary voltage Vp(rms) = 115 V.
• Ideal transformer (ignoring losses and regulation for this calculation).

Concept / Approach:For an ideal transformer: Vs/Vp = Ns/Np. After getting Vs(rms), convert to peak using Vp(peak) = Vrms * sqrt(2). We apply this to the secondary value.

Step-by-Step Solution:1) Use ratio: Vs(rms) = Vp(rms) * (Ns/Np) = 115 * 4 = 460 V (rms).2) Convert rms to peak: Vpeak = Vrms * sqrt(2) ≈ 460 * 1.414.3) Compute: 460 * 1.414 ≈ 650.44 V.4) Round to the closest option: 651 V.

Verification / Alternative check:Check plausibility: a 4x step-up from 115 V yields 460 V rms; a peak near 1.414 times that is expected near 650 V. The result is consistent with sinusoidal assumptions.

Why Other Options Are Wrong:700 V and 707 V suggest misuse of 115 * 1.414 or misapplied ratios. 208 V is far too small and would correspond to a step-down, not step-up. “None of the above” is unnecessary since 651 V matches the correct rounded value.

Common Pitfalls:Confusing rms with peak; forgetting to apply the turns ratio before converting; using 2 instead of sqrt(2) for peak conversion.

Final Answer:651 V