Reactance of a Capacitor

Introduction:
Reactance is a measure of the opposition offered by a component to the flow of alternating current (AC). In the case of a capacitor, its reactance is inversely proportional to the frequency of the AC source.

Formula:
The reactance (Xc) of a capacitor can be calculated using the formula:
Xc = 1 / (2 * π * f * C)

Where:
Xc = Reactance of the capacitor
π = Pi (approximately 3.14159)
f = Frequency of the AC source
C = Capacitance of the capacitor

Given:
Capacitance (C) = 50 pF = 50 × 10^(-12) F
Frequency (f) = 1 kHz = 1 × 10^3 Hz

Calculations:
Using the given values in the formula, we can calculate the reactance of the capacitor as follows:

Xc = 1 / (2 * π * f * C)
= 1 / (2 * 3.14159 * 1 × 10^3 * 50 × 10^(-12))
≈ 1 / (314.159 * 5 × 10^(-11))
≈ 6.37 × 10^6 Ω

Therefore, the reactance of the capacitor is approximately 6.37 megaohms (Ω).

Explanation:
The reactance of a capacitor is determined by its capacitance and the frequency of the AC source. In this case, the given capacitor has a capacitance of 50 pF (picofarads) and is connected to an AC source with a frequency of 1 kHz (kilohertz).

Using the formula for reactance, we substitute the given values and calculate the reactance of the capacitor. The reactance is found to be approximately 6.37 megaohms (Ω).

Summary:
The reactance of a capacitor is inversely proportional to the frequency of the AC source. In this case, the reactance of a 50 pF capacitor connected to a 1 kHz AC source is approximately 6.37 megaohms (Ω).