Physics

Physics

Problem

A capacitor has a capacitive reactance XCX_C when it is connected to an AC source of frequency ff. The frequency of the source is now doubled. (i) Write an expression for the new capacitive reactance in terms of XCX_C. (ii) Hence calculate the percentage change in the capacitive reactance.
Intuitive explanation

Capacitive reactance depends inversely on frequency through the formula XC=12πfCX_C = \frac{1}{2\pi f C}. When frequency doubles, you're dividing the denominator by a smaller number, so the reactance shrinks proportionally. The key is recognizing this reciprocal relationship: doubling ff cuts XCX_C in half, which then lets you find the percentage change directly.

Intuitive explanation

Capacitive reactance depends inversely on frequency through the formula XC=12πfCX_C = \frac{1}{2\pi f C}. When frequency doubles, you're dividing the denominator by a smaller number, so the reactance shrinks proportionally. The key is recognizing this reciprocal relationship: doubling ff cuts XCX_C in half, which then lets you find the percentage change directly.

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