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?
Electronics
Transformers
Difficulty: Easy
Choose an option
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A13 Ω
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B7.8 Ω
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C78 Ω
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D1.3 Ω
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E28 Ω
Answer
Correct Answer: 13 Ω
Explanation
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:
Compute the square of the turns ratio: (Np/Ns)^2 = (1/6)^2 = 1/36.R_in = (1/36) * 470 Ω ≈ 13.0556 Ω.Rounded to the nearest whole ohm, R_in ≈ 13 Ω.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