Question

A 0.20-,uF capacitor is connected across the terminals of a variable-frequency oscillator. At what frequency is its reactance 84 Ω? What will the reactance be if the frequency is then tripled?

Answer 1

The reactance of the capacitor is given by

$$X_C = \dfrac{1}{2\pi f C}$$

where $f$ is the frequency, and $C = 0.2\mu F = 0.2\times 10^{-6}F$. Since $X_C = 84\Omega$, the frequency is

$$f = \dfrac{1}{2\pi X_C C}\\ f = \dfrac{1}{2\pi \cdot 84 \cdot 0.2\times 10^{-6}} \approx 9.47\times 10^3Hz = 9.47\space kHz$$

Answer. 9.47 kHz.