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

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

Options:

Correct Answer: It doubles

Exam Year: 2023

Solution:

The reactance of an inductor is given by XL = ωL. If frequency is doubled, reactance also doubles.

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.

Inductive Reactance – Inductive reactance (XL) is the opposition that an inductor presents to alternating current, which is directly proportional to the frequency (f) of the AC source and the inductance (L) of the inductor.
Frequency and Reactance Relationship – The relationship between frequency and reactance is given by the formula XL = 2πfL, indicating that if the frequency is doubled, the reactance will also change accordingly.