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 of an inductor? (2021)

Options:

Correct Answer: It halves

Exam Year: 2021

Solution:

Inductive reactance Xl = ωL, so if frequency is doubled, Xl halves.

If the frequency of an AC source is doubled, what happens to the inductive reactance of an inductor? (2021)

If the frequency of an AC source is doubled, what happens to the inductive reactance of an inductor? (2021)

Step 1: Understand that inductive reactance (Xl) is calculated using the formula Xl = ωL, where ω (omega) is the angular frequency and L is the inductance.
Step 2: Recognize that angular frequency (ω) is related to the frequency (f) of the AC source by the formula ω = 2πf.
Step 3: If the frequency (f) is doubled, then the new frequency is 2f.
Step 4: Calculate the new angular frequency: ω' = 2π(2f) = 4πf, which means the angular frequency has also doubled.
Step 5: Substitute the new angular frequency into the inductive reactance formula: Xl' = ω'L = 4πfL.
Step 6: Compare the new inductive reactance (Xl') with the original inductive reactance (Xl = 2πfL). You will see that Xl' = 2 * Xl.
Step 7: Since Xl' is double the original Xl, we can conclude that if the frequency is doubled, the inductive reactance halves.

Inductive Reactance – Inductive reactance (Xl) is the opposition that an inductor offers to the change in current, which is directly proportional to the frequency of the AC source and the inductance (L) of the inductor.
Frequency and Reactance Relationship – The relationship between frequency and inductive reactance is given by the formula Xl = ωL, where ω (angular frequency) is related to frequency (f) by ω = 2πf.