Reflected resistance: A transformer has a 1:6 turns ratio (Np:Ns = 1:6) and a 470 Ω load on the secondary. What is the equivalent load resistance seen at the primary?

Introduction / Context:Transformers reflect impedances by the square of the turns ratio. This principle is pivotal in matching sources to loads, optimizing power transfer, and designing audio/RF interfaces.

Given Data / Assumptions:

• Turns ratio Np:Ns = 1:6.
• Secondary (load-side) resistance RL = 470 Ω.
• Ideal transformer approximation.

Concept / Approach:Reflected (equivalent) resistance at the primary is R_in = (Np/Ns)^2 * RL. Because Np < Ns, the resistance seen at the primary will be much smaller than RL (step-down of resistance by the squared ratio).

Step-by-Step Solution:

Verification / Alternative check:As a quick check, 36 * 13 Ω ≈ 468 Ω, close to the actual 470 Ω, confirming the arithmetic.

Why Other Options Are Wrong:

• 78 Ω or 7.8 Ω or 1.3 Ω: These correspond to using the wrong ratio or misplacing the decimal.
• 28 Ω: Not consistent with the required 1/36 factor.

Common Pitfalls:

• Using Ns/Np instead of Np/Ns in the square.
• Forgetting to square the turns ratio when reflecting resistance.

Final Answer:13 Ω