A.C. (alternating current) fundamentals in a purely capacitive circuit involve understanding how capacitors behave when connected to an AC voltage source. In such circuits, the main component is a capacitor, which is an electronic component designed to store and release electrical energy. Here's an overview of how a purely capacitive circuit behaves in an AC system:
Capacitor Reactance (Xc): In a purely capacitive circuit, the primary opposition to the flow of AC current is the reactance of the capacitor. The reactance of a capacitor is given by the formula:
=
1
2
Xc=
2πfC
1
Where:
Xc is the capacitive reactance (measured in ohms, Ω).
f is the frequency of the AC signal (measured in hertz, Hz).
C is the capacitance of the capacitor (measured in farads, F).
The capacitive reactance increases with decreasing frequency and decreasing capacitance, which means that lower-frequency signals and smaller capacitors will present higher opposition to the flow of current.
Current and Voltage Relationship: In a purely capacitive circuit, the current leads the voltage by 90 degrees. This phase relationship is a result of the charging and discharging behavior of the capacitor. When the AC voltage source is at its peak, the capacitor is initially uncharged, and the current flows to charge it. As the voltage decreases, the capacitor discharges, and the current decreases as well. This leads to a current waveform that is 90 degrees ahead of the voltage waveform.
Impedance (Z): Impedance is the total opposition that a circuit offers to the flow of AC current, similar to resistance in a DC circuit. In a purely capacitive circuit, impedance is also frequency-dependent and is given by:
=
Z=Xc
Since there is no resistance in a purely capacitive circuit, the impedance is purely reactive.
Phase Angle: The phase angle between the voltage and current waveforms in a purely capacitive circuit is 90 degrees. This phase difference between the voltage and current is a characteristic feature of capacitive circuits and is a result of the charging and discharging behavior of the capacitor.
Power Factor: In a purely capacitive circuit, the power factor is leading (greater than 1) and is denoted as
=
(
)
pf=cos(ϕ), where
ϕ is the phase angle between voltage and current. Since the current leads the voltage by 90 degrees, the power factor is a positive value.
Apparent Power (S) and Reactive Power (Q): Since the power factor is leading, the reactive power (Q) is positive. The apparent power (S) is the product of voltage, current, and power factor. In a purely capacitive circuit, the apparent power is equal to the reactive power (S = Q).
Understanding these concepts is essential for designing and analyzing AC circuits that involve capacitive elements. Keep in mind that in practical circuits, capacitors are often combined with other components, such as resistors and inductors, to create more complex circuits with diverse behaviors.