Final answer:
The impedance of a 3 mH inductor at 636 Hz is 12.0 ohms, represented as 12.0Ω∶ or j12.0Ω.
Step-by-step explanation:
To calculate the impedance for a 3 mH inductor at 636 Hz, we use the formula for inductive reactance ℞, which is given by ℞ = 2πfL. Here, ℞ is the inductive reactance, f is the frequency in hertz, and L is the inductance in henrys. For an inductor, the impedance is purely reactive (imaginary) and is represented by ℞∶ or j℞.
Applying the provided values:
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- f = 636 Hz
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- L = 3 mH = 3 × 10⁻³ H
We can calculate the inductive reactance:
℞ = 2π × 636 Hz × 3 × 10⁻³ H
= 2π × 636 × 3×10⁻³
= 12.0 ohms
Therefore, the impedance of a 3 mH inductor at a frequency of 636 Hz is 12.0 ohms represented as 12.0Ω∶ or j12.0Ω.