In a pure inductive circuit, the relationship between power and various electrical parameters can be described using a power curve. Let's explore how power behaves in a pure inductive circuit.
A pure inductive circuit consists of an inductor connected to an AC voltage source. An inductor is a passive component that resists changes in current. In an AC circuit, the voltage across an inductor varies sinusoidally with time, leading the current to also vary sinusoidally, but lagging the voltage by 90 degrees.
Here's what the power curve for a pure inductive circuit looks like:
Instantaneous Power: The instantaneous power (P) in an AC circuit can be calculated using the formula:
P(t) = V(t) * I(t) * cos(θ)
Where:
P(t) is the instantaneous power at time t.
V(t) is the instantaneous voltage at time t.
I(t) is the instantaneous current at time t.
θ is the phase angle between voltage and current (90 degrees in a pure inductive circuit).
Power Factor: In a pure inductive circuit, the power factor (PF) is defined as the cosine of the phase angle (θ) between voltage and current. Since the phase angle is 90 degrees, the power factor in a pure inductive circuit is 0. This means that the real power (the power that does useful work) is zero, and the apparent power (the product of voltage and current) is equal to the reactive power (the power that is stored and released in the inductor).
Reactive Power: The reactive power (Q) in a pure inductive circuit is given by:
Q = Vrms * Irms
Where:
Vrms is the root mean square (RMS) voltage.
Irms is the RMS current.
Apparent Power: The apparent power (S) in a pure inductive circuit is the product of the RMS voltage and RMS current:
S = Vrms * Irms
Since the power factor in a pure inductive circuit is 0, the power curve shows that real power (P) is zero throughout the AC cycle. The reactive power (Q) is constantly exchanged between the source and the inductor, leading to a sinusoidal curve for reactive power.
In summary, the power curve for a pure inductive circuit shows zero real power, a sinusoidal reactive power curve, and a power factor of 0. This implies that the circuit consumes reactive power but does not perform any useful work.