An audio transformer has a turns ratio Np:Ns = 9:1 (primary to secondary). What is its impedance ratio Zp:Zs?

Introduction / Context:
Transformers scale both voltage and impedance. The impedance seen at one winding due to a load on the other is related to the square of the turns ratio. This property is widely used to match speakers to amplifiers and to optimize power transfer.

Given Data / Assumptions:

• Turns ratio Np:Ns = 9:1.
• We want Zp:Zs, the impedance ratio referred from secondary to primary.
• Ideal transformer model (lossless, perfect coupling) for the relationship.

Concept / Approach:
Impedance transformation follows Zp/Zs = (Np/Ns)^2. With Np/Ns = 9, square to obtain the impedance ratio. This means a 1 Ω load on the secondary appears as 81 Ω at the primary.

Step-by-Step Solution:
Compute turns ratio a = Np/Ns = 9.Apply formula: Zp/Zs = a^2.Calculate: a^2 = 9^2 = 81.

Verification / Alternative check:
Voltage scales by 9, current scales by 1/9, so impedance (V/I) scales by 9 / (1/9) = 81, confirming the square law.

Why Other Options Are Wrong:
85, 6, 9: do not follow the square-of-turns rule for 9:1.None of the above: incorrect because 81 is correct.

Common Pitfalls:
Using the turns ratio directly instead of squaring; mixing up primary/secondary order leading to inversion.

Final Answer:
81