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

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Question: If the frequency of an AC source is doubled, what happens to the inductive reactance? (2014)

Options:

Correct Answer: It halves

Solution:

Inductive reactance XL = 2πfL, so if frequency f is doubled, XL halves.

If the frequency of an AC source is doubled, what happens to the inductive reactance? (2014)

If the frequency of an AC source is doubled, what happens to the inductive reactance? (2014)

Step 1: Understand what inductive reactance (XL) is. It is a measure of how much an inductor resists the flow of alternating current (AC).
Step 2: Know the formula for inductive reactance: XL = 2πfL, where 'f' is the frequency and 'L' is the inductance.
Step 3: Identify what happens when the frequency 'f' is doubled. If f becomes 2f, we will substitute this into the formula.
Step 4: Substitute the new frequency into the formula: XL = 2π(2f)L = 4πfL.
Step 5: Compare the new inductive reactance (4πfL) with the original (2πfL). Notice that if frequency is doubled, the inductive reactance is not doubled but rather it becomes 4 times the original value.
Step 6: Realize that the question asks what happens to XL when frequency is doubled. Since XL is directly proportional to frequency, if frequency is doubled, XL increases.
Step 7: Conclude that if frequency is doubled, the inductive reactance increases, not halves.

Inductive Reactance – Inductive reactance (XL) is the opposition that an inductor presents to alternating current (AC) due to its inductance and is directly proportional to the frequency of the AC source.
Frequency and Reactance Relationship – The relationship between frequency and inductive reactance is given by the formula XL = 2πfL, indicating that as frequency increases, inductive reactance increases, and vice versa.