# A.C. Fundamentals - Power in Pure Capacitive Circuit

A.C. Fundamentals - Power in Pure Capacitive Circuit

In an AC (alternating current) circuit, power in a pure capacitive circuit is an interesting concept. A pure capacitive circuit consists of only a capacitor and a sinusoidal AC voltage source. Unlike resistors, capacitors don't dissipate energy in the form of heat, so the concept of power in a pure capacitive circuit might seem a bit counterintuitive.

In a capacitive circuit, the current leads the voltage by 90 degrees. This means that the current waveform reaches its peak before the voltage waveform. As a result, the instantaneous power can be positive and negative over each cycle of the AC waveform.

However, the average power over a complete AC cycle in a pure capacitive circuit is always zero. This is because energy is stored in the electric field of the capacitor when the voltage is increasing and then returned to the circuit when the voltage is decreasing, resulting in a net transfer of energy back and forth between the capacitor and the source without any net energy consumption or dissipation.

Mathematically, the instantaneous power in an AC circuit can be calculated using the following formula:

Instantaneous Power = Voltage (V) Ă Current (I) = V(t) Ă I(t)

For a pure capacitive circuit, the current leads the voltage by 90 degrees, so the power factor (cosine of the phase angle between voltage and current) is zero. This leads to the average power over a full cycle being zero.

In summary, in a pure capacitive circuit:

The current leads the voltage by 90 degrees.
Instantaneous power can be both positive and negative.
The average power over a complete AC cycle is always zero.

It's important to note that while the average power is zero, the circuit does experience reactive power, which contributes to the overall power flow in the AC system and affects aspects like voltage regulation and power factor correction. Reactive power is essential to maintain the proper functioning of AC networks, but it doesn't involve actual energy consumption or dissipation as in the case of real power (which is associated with resistive elements).

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