Answer to Question #152017 in Physics for maxwell

Question

A 40-mH inductor has a resistance of 25 S2. What are its
reactance and impedance at the frequencies of 0 Hz (dc), 60
Hz, and 500 Hz?

Answer 1

The reactance is:

$$X_L = 2\pi fL$$

where $f$ is the frequency, and $L = 40mH = 0.04H$ is the inductance of the inductor. Thus, for different frequencies obtain:

$$X_L =2\pi\cdot 0\cdot 0.04 = 0\Omega\\ X_L =2\pi\cdot 60\cdot 0.04 \approx 15.1\Omega\\ X_L =2\pi\cdot 500\cdot 0.04 \approx 125.7\Omega$$

The impedance is:

$$Z = \sqrt{R^2 + X_L^2}$$

where $R = 25\Omega$ is the resistance of the inductor. Thus, for different $X_L$ from the previous step obtain:

$$Z = \sqrt{25^2 + 0^2} = 25\Omega\\ Z = \sqrt{25^2 + 15.1^2} \approx 29.2\Omega\\ Z = \sqrt{25^2 + 125.7^2} \approx 128.1\Omega$$