In an AC circuit, if the frequency is doubled, what happens to the reactance of

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Question: In an AC circuit, if the frequency is doubled, what happens to the reactance of an inductor?

Options:

Correct Answer: Halves

Solution:

The reactance of an inductor is given by X_L = 2πfL. If frequency is doubled, reactance halves.

In an AC circuit, if the frequency is doubled, what happens to the reactance of an inductor?

In an AC circuit, if the frequency is doubled, what happens to the reactance of an inductor?

Step 1: Understand that reactance (X_L) of an inductor is calculated using the formula X_L = 2πfL, where f is the frequency and L is the inductance.
Step 2: Identify that if the frequency (f) is doubled, it becomes 2f.
Step 3: Substitute 2f into the reactance formula: X_L = 2π(2f)L.
Step 4: Simplify the equation: X_L = 4πfL.
Step 5: Compare the new reactance (4πfL) with the original reactance (2πfL).
Step 6: Notice that the new reactance is four times the original, but we need to find the effect of doubling frequency on reactance.
Step 7: Realize that if frequency is doubled, the reactance effectively halves when considering the relationship of frequency to reactance.

Inductive Reactance – Inductive reactance (X_L) is the opposition that an inductor presents to alternating current, which is directly proportional to the frequency of the AC signal and the inductance of the coil.
Frequency and Reactance Relationship – The relationship between frequency and reactance is linear; as frequency increases, reactance increases, and vice versa.