If the frequency of an AC source is doubled, what happens to the reactance of an

If the frequency of an AC source is doubled, what happens to the reactance of an inductor? (2023)

If the frequency of an AC source is doubled, what happens to the reactance of an inductor? (2023)

Step 1: Understand that reactance (XL) of an inductor depends on frequency (f) and inductance (L).
Step 2: The formula for reactance is XL = ωL, where ω (omega) is the angular frequency.
Step 3: Angular frequency (ω) is calculated as ω = 2πf, where f is the frequency in hertz.
Step 4: If the frequency (f) is doubled, the new frequency becomes 2f.
Step 5: Calculate the new angular frequency: ω' = 2π(2f) = 4πf.
Step 6: Substitute the new angular frequency into the reactance formula: XL' = ω'L = 4πfL.
Step 7: Compare the new reactance (XL') with the original reactance (XL = 2πfL).
Step 8: Notice that XL' = 2 * (2πfL) = 2 * XL, meaning the reactance doubles.

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