Step-down calculation: A transformer has a 110 V primary and a 15:1 turns ratio (primary:secondary). With RL = 120 Ω, what is the approximate load voltage?
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A73 V
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B7.3 V
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C88 V
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D880 V
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E11 V
Answer
Correct Answer: 7.3 V
Explanation
Introduction / Context:Here we apply the turns ratio to obtain the secondary voltage of a step-down transformer under load. For most practical cases with modest current and low winding resistance, the ideal ratio gives a good approximation of the load voltage.
Given Data / Assumptions:
- Vp = 110 V (RMS).
- Turns ratio Np:Ns = 15:1.
- Load RL = 120 Ω; assume ideal transformer behavior for voltage estimation.
Concept / Approach:For an ideal transformer, Vs = Vp * (Ns / Np). A 15:1 primary:secondary ratio means one-fifteenth of the primary voltage appears on the secondary winding.
Step-by-Step Solution:
Compute Ns/Np = 1 / 15.Vs = 110 * (1 / 15) ≈ 7.33 V.Rounded to one decimal place, ≈ 7.3 V across RL.Verification / Alternative check:Secondary current would be Is ≈ Vs / RL ≈ 7.33 / 120 ≈ 61 mA. Reflected to primary, Ip ≈ Is / 15 ≈ 4.1 mA; apparent power ≈ 0.45 VA—small, justifying negligible regulation for this estimate.
Why Other Options Are Wrong:
- 73 V: Off by a factor of 10.
- 88 V and 880 V: Do not follow the 15:1 step-down relation.
- 11 V: Would correspond to 10:1, not 15:1.
Common Pitfalls:
- Mistaking 15:1 as secondary:primary, which would predict a step-up.
- Using peak instead of RMS values.
Final Answer:7.3 V