If the frequency of an AC source is doubled, what happens to the reactance of a

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Question: If the frequency of an AC source is doubled, what happens to the reactance of a capacitor? (2023)

Options:

Correct Answer: It halves

Exam Year: 2023

Solution:

The capacitive reactance Xc = 1/(2πfC) halves when the frequency f is doubled.

If the frequency of an AC source is doubled, what happens to the reactance of a capacitor? (2023)

If the frequency of an AC source is doubled, what happens to the reactance of a capacitor? (2023)

Step 1: Understand that reactance is a measure of how much a capacitor resists the flow of alternating current (AC).
Step 2: Know the formula for capacitive reactance, which is Xc = 1/(2πfC), where Xc is the reactance, f is the frequency, and C is the capacitance.
Step 3: Identify that if the frequency (f) is doubled, we replace f with 2f in the formula.
Step 4: Substitute 2f into the formula: Xc = 1/(2π(2f)C).
Step 5: Simplify the equation: Xc = 1/(4πfC).
Step 6: Compare the new reactance (1/(4πfC)) with the original reactance (1/(2πfC)).
Step 7: Notice that the new reactance is half of the original reactance, meaning it has decreased.

Capacitive Reactance – Capacitive reactance (Xc) is the opposition that a capacitor offers to the flow of alternating current (AC) and is inversely proportional to the frequency of the AC source and the capacitance.
Frequency and Reactance Relationship – Doubling the frequency of an AC source results in halving the capacitive reactance, as described by the formula Xc = 1/(2πfC).