In an AC (alternating current) circuit, the relationship between voltage, current, and power can be complex due to the presence of reactive components like inductors (L) and capacitors (C). In an R-L (resistor-inductor) series circuit, the interaction between resistance and inductance creates a phase difference between voltage and current, which affects the power curve.
Here's how the power curve behaves in an R-L series circuit:
Phase Relationship: In an R-L circuit, the current lags behind the voltage due to the presence of inductance. This lag is represented by a phase angle (θ) between the voltage and current waveforms.
Instantaneous Power: The instantaneous power in an AC circuit can be calculated using the formula: P(t) = V(t) * I(t), where V(t) is the instantaneous voltage and I(t) is the instantaneous current.
Power Factor: The power factor (PF) is the cosine of the phase angle (θ) between voltage and current. It's a measure of how effectively the circuit converts the supplied electrical energy into useful work. A higher power factor indicates better efficiency.
PF = cos(θ)
Power factor values range between 0 and 1. A purely resistive circuit (no inductance or capacitance) has a power factor of 1 (cos(0°) = 1), indicating that voltage and current are in phase. In contrast, in an R-L circuit, the power factor will be less than 1 due to the phase angle.
Active Power (Real Power): The active power, also known as real power (P), is the component of power that is converted into useful work. It's given by the formula:
P = Vrms * Irms * cos(θ)
Here, Vrms is the root mean square (RMS) voltage, Irms is the RMS current, and θ is the phase angle.
Reactive Power: Reactive power (Q) is the component of power that does not perform any useful work but is needed to establish the magnetic field in inductive elements or the electric field in capacitive elements. It's given by the formula:
Q = Vrms * Irms * sin(θ)
Reactive power is measured in volt-amperes reactive (VAR).
Apparent Power: Apparent power (S) is the vector sum of active power and reactive power. It's the total power flowing in the circuit and is given by:
S = Vrms * Irms
Apparent power is measured in volt-amperes (VA).
The power curve in an R-L series circuit can be represented by a power triangle, where the active power, reactive power, and apparent power form the sides of the triangle. The angle θ between active power and apparent power vectors represents the phase difference between voltage and current.
Remember that in an R-L circuit, the power factor is generally less than 1 due to the phase shift between voltage and current. This phase shift causes a non-sinusoidal behavior of the power curve, where power fluctuates over time.