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why the impedance ratio of a transformer is the square of the turns ratio.

why the impedance ratio of a transformer is the square of the turns ratio.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Given the attached image, please explain why the impedance ratio of a transformer is the square of the turns ratio.

**Inductive Reactance Formula** The inductive reactance (\(X_L\)) is given by the formula: \[ X_L = 2\pi f L = 2\pi f \frac{N^2 \mu A}{l} \] - **\(X_L\)**: Inductive reactance, measured in ohms (Ω). - **\(f\)**: Frequency of the alternating current, measured in hertz (Hz). - **\(L\)**: Inductance, measured in henrys (H). - **\(N\)**: Number of turns in the coil. - **\(\mu\)**: Permeability of the core material. - **\(A\)**: Cross-sectional area of the coil, measured in square meters (m²). - **\(l\)**: Length of the coil, measured in meters (m). This formula explains how inductive reactance depends on frequency and coil characteristics, affecting how the coil impedes the flow of current in an AC circuit.
Transcribed Image Text:**Inductive Reactance Formula** The inductive reactance (\(X_L\)) is given by the formula: \[ X_L = 2\pi f L = 2\pi f \frac{N^2 \mu A}{l} \] - **\(X_L\)**: Inductive reactance, measured in ohms (Ω). - **\(f\)**: Frequency of the alternating current, measured in hertz (Hz). - **\(L\)**: Inductance, measured in henrys (H). - **\(N\)**: Number of turns in the coil. - **\(\mu\)**: Permeability of the core material. - **\(A\)**: Cross-sectional area of the coil, measured in square meters (m²). - **\(l\)**: Length of the coil, measured in meters (m). This formula explains how inductive reactance depends on frequency and coil characteristics, affecting how the coil impedes the flow of current in an AC circuit.
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