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Capacitance is a fundamental concept in the study of capacitors in electrical circuits. It represents a capacitor's ability to store electrical charge. The capacitance, denoted by the letter \( C \), is measured in Farads (F). A higher capacitance means the capacitor can hold more charge at a particular voltage.
Capacitors find use in various practical applications such as filtering noise from power supply lines and tuning circuits in radios. The value of the capacitance depends on factors like the surface area of the plates, the distance between them, and the dielectric material used.

• Larger surface area - higher capacitance
• Increased distance - lower capacitance
• Material properties - affects capacitance

Remember, capacitance is crucial because it influences how capacitors react to alternating current in a circuit, leading us directly to the concept of capacitive reactance!

In electrical circuits, frequency is the rate at which an alternating current (AC) signal cycles through a complete sequence. This is measured in Hertz (Hz), with 1 Hz representing one complete cycle per second. Frequency is a key factor in AC circuits, affecting how components like capacitors and inductors respond.
When the frequency increases, the time for one cycle decreases, impacting how quickly a capacitor charges and discharges. In the context of capacitive reactance,

• Higher frequency - lower reactance
• Lower frequency - higher reactance

Understanding frequency is crucial because it directly influences the reactance of a capacitor. It leads us to observe interesting behaviors when manipulating circuit parameters, such as when capacitance and frequency are doubled, effectively lowering reactance in our given problem.

The reactance formula defines the opposition that a capacitor presents to alternating current, known as capacitive reactance. The formula is given as \( X_c = \frac{1}{2\pi f C} \), where:

• \(X_c\) is the capacitive reactance
• \(f\) is the frequency
• \(C\) is the capacitance

The relationship between these variables indicates that reactance is inversely proportional to both frequency and capacitance. This means that as either frequency or capacitance increases, the reactance decreases.
In our exercise, when both capacitance and frequency double, substituting these new values into the reactance formula reveals that the reactance is reduced by a factor of four. Recognizing how each part of the formula contributes to reactance helps in accurately predicting how changes in circuit parameters will affect its behavior in practical scenarios.