If the frequency of an AC source is doubled, how does the inductive reactance ch

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Question: If the frequency of an AC source is doubled, how does the inductive reactance change? (2020)

Options:

Correct Answer: Halves

Solution:

Xl = 2πfL; if f is doubled, Xl also doubles.

If the frequency of an AC source is doubled, how does the inductive reactance change? (2020)

If the frequency of an AC source is doubled, how does the inductive reactance change? (2020)

Step 1: Understand what inductive reactance (Xl) is. It is the opposition that an inductor offers to 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 need to 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 the new value is double the original value.
Step 6: Conclude that if the frequency is doubled, the inductive reactance also doubles.

Inductive Reactance – Inductive reactance (Xl) is the opposition that an inductor presents to alternating current (AC) due to its inductance (L) and the frequency (f) of the AC source.
Frequency and Reactance Relationship – The relationship between frequency and inductive reactance is direct; as frequency increases, inductive reactance increases proportionally.