Transformer step-down calculation: a transformer has a turns ratio of 5:1 (primary:secondary). The primary is 120 V (rms). What is the secondary voltage (rms)?

Introduction / Context:
Transformers scale AC voltages according to their turns ratio. Quick mental math with ratios is invaluable for power supplies, instrumentation, and isolation applications. This question asks for the secondary rms voltage of a 5:1 step-down transformer driven by 120 Vrms.

Given Data / Assumptions:

• Turns ratio Np:Ns = 5:1 (step-down).
• Primary voltage Vp(rms) = 120 V.
• Ideal transformer approximation (neglect losses and regulation).

Concept / Approach:
For ideal transformers, Vs/Vp = Ns/Np. Because Ns/Np = 1/5, the secondary voltage is one-fifth of the primary rms voltage.

Step-by-Step Solution:
1) Compute ratio: Ns/Np = 1/5 = 0.2.2) Apply to voltage: Vs = Vp * (Ns/Np) = 120 * 0.2.3) Calculate: 120 * 0.2 = 24.4) Secondary rms voltage is 24 V.

Verification / Alternative check:
Reverse-check: If Vs = 24 V, then Vp/Vs = 120/24 = 5, matching the turns ratio 5:1.

Why Other Options Are Wrong:
12 V implies a 10:1 step-down; 18 V and 30 V correspond to other ratios; “None of the above” is invalid since 24 V fits exactly.

Common Pitfalls:
Inverting the ratio (using 5 instead of 1/5) or confusing rms and peak values. The problem explicitly asks for rms, so no sqrt(2) conversion is needed.

Final Answer:
24 V