Turns ratio for stepping 110 V AC down to 20 V AC: what transformer turns ratio is required (Np:Ns)?

Introduction / Context:
Transformer design often begins with the desired voltage ratio. The primary-to-secondary turns ratio Np:Ns directly sets the output voltage under ideal conditions, a foundational concept for power converters and isolation transformers.

Given Data / Assumptions:

• Input (primary) voltage Vp = 110 V AC.
• Desired output (secondary) voltage Vs = 20 V AC.
• Ideal transformer approximation (no losses).

Concept / Approach:
Ideal relation: Vp/Vs = Np/Ns. Rearranging gives the turns ratio directly. A step-down transformer requires more primary turns than secondary turns, so the ratio should be > 1.

Step-by-Step Solution:

Verification / Alternative check:
Back-check voltage: Vs = Vp / 5.5 = 110 / 5.5 = 20 V, as required.

Why Other Options Are Wrong:

• 0.18 and 0.018: These are Ns:Np-like fractions, implying step-up, not step-down.
• 18: Would give Vs ≈ 110/18 ≈ 6.1 V, too low.
• 2.2: Would give Vs = 50 V, not 20 V.

Common Pitfalls:

• Confusing Np:Ns with Ns:Np; always match the ratio to Vp:Vs for ideal cases.
• Ignoring regulation and load; those affect real outputs but not the ideal turns ratio.

Final Answer:
5.5