If the inductance of a coil is doubled, what happens to its inductive reactance

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Question: If the inductance of a coil is doubled, what happens to its inductive reactance at a constant frequency? (2022)

Options:

Correct Answer: It doubles

Exam Year: 2022

Solution:

Inductive reactance (X_L) is given by X_L = 2πfL. If the inductance (L) is doubled, X_L will also double.

If the inductance of a coil is doubled, what happens to its inductive reactance at a constant frequency? (2022)

If the inductance of a coil is doubled, what happens to its inductive reactance at a constant frequency? (2022)

Step 1: Understand what inductive reactance (X_L) is. It is a measure of how much a coil resists the flow of alternating current (AC) due to its inductance.
Step 2: Know the formula for inductive reactance: X_L = 2πfL, where 'f' is the frequency and 'L' is the inductance.
Step 3: Identify that if the inductance (L) is doubled, we can represent this as L' = 2L.
Step 4: Substitute the new inductance into the formula: X_L' = 2πf(2L) = 2(2πfL) = 2X_L.
Step 5: Conclude that if the inductance is doubled, the inductive reactance will also double.

Inductive Reactance – Inductive reactance (X_L) is the opposition that an inductor presents to alternating current (AC) due to its inductance (L) and the frequency (f) of the AC signal.
Relationship Between Inductance and Reactance – The formula X_L = 2πfL shows that inductive reactance is directly proportional to both the inductance and the frequency.