In AC (alternating current) circuits, power in a pure inductive element behaves differently compared to other circuit components like resistors and capacitors. A pure inductor is an idealized component that consists of only inductance and negligible resistance or capacitance.
In a pure inductive circuit, such as an ideal inductor connected to an AC power source, the voltage and current are out of phase by 90 degrees. This means that the current through the inductor lags behind the voltage across it. Here's how power behaves in a pure inductive circuit:
Instantaneous Power: The instantaneous power in an inductor can be calculated using the formula:
(
)
=
p(t)=vi
Where:
(
)
p(t) is the instantaneous power at time
t
v is the instantaneous voltage across the inductor at time
t
i is the instantaneous current through the inductor at time
t
Average Power: In a pure inductive circuit, the average power over a complete AC cycle is zero. This is because the power is constantly shifting between the inductor and the source without being dissipated as heat or doing useful work.
Reactive Power: In a pure inductive circuit, the power is not consumed or dissipated as it is in a resistor. Instead, the inductor stores and releases energy in the form of a magnetic field. The concept of reactive power arises in AC circuits with inductors and capacitors. Reactive power is not directly converted into useful work but plays a crucial role in maintaining the overall power factor of the circuit.
Power Factor: The power factor of an AC circuit is a measure of how effectively the circuit converts electric power into useful work. In the case of a pure inductive circuit, the power factor is lagging, and its value is typically expressed as a lagging angle (θ) between the voltage and current waveforms. The power factor for a pure inductive circuit is usually considered to be zero.
Mathematically, the power factor (
PF) for a pure inductive circuit is given by:
=
cos
=
cos
90
°
=
0
PF=cosθ=cos90°=0
In summary, in a pure inductive circuit, the average power over a complete AC cycle is zero, and the power is stored and released in the form of a magnetic field without being dissipated as heat. The concept of reactive power and power factor are important considerations in AC circuit analysis and power distribution systems.