Lecture Notes on Power in AC Circuits

Overview

• Discussed currents: Resistive, Inductive, combined with Pythagorean theorem
• Determined total impedance
• Focused on different types of power

Types of Power

Apparent Power

• Measured in voltage
• Needs to be provided by the circuit

True Power (Working Power)

• Real power doing actual work (heat, light, motion)
• Across the resistive component

Reactive Power

• Voltage reactance, e.g., from an inductor
• Stored and released, not doing actual work
• Still needs to be provided by the circuit

In-Phase and Out-of-Phase Currents

• Resistive current: In phase with voltage
• Inductive current: Out of phase (90 degrees)
• Combined currents: Neither fully in-phase nor fully out-of-phase
  • More inductive current results in overall current closer to 90 degrees

Power Calculation

• Positive power: Both voltage and current are positive or both are negative
• Negative power: Voltage and current have opposite signs
• Overall net power is positive due to resistive component
• No real work done if purely inductive (half positive half negative)

Using Ohm's Law for Power

• Power as a function of voltage and current (V x I), or V² divided by ohms, or I² times resistance
• Calculations for power components:
  • True Power: 288 W (watts)
  • Reactive Power: 381.6 VARs (volt-ampere reactive)
  • Apparent Power: 477.6 VA

Power Triangle

• True Power (P): Resistive components, horizontal line
• Reactive Power (Q): Inductive components, vertical line
• Apparent Power (S): Vector sum (hypotenuse)
  • Formula: S^2 = P^2 + Q^2

Power Factor

• Efficiency of power use in the circuit
• Ratio of True Power to Apparent Power
  • Example: 288 W / 477.6 VA = ~60.3%
• Relation between power factor and angle theta (cosine relationship)
  • Adjacent side / Hypotenuse = Power factor
  • Calculate angle: arccos(0.603) ≈ 52.9°
  • Current lags voltage by 52.9°
  • Efficiency and phase shift interpretation

Additional Considerations

• Inductive power triangles generally point up
• Capacitive power triangles generally point down
• RL circuit current triangle in parallel has voltage as reference, with current lagging by 90 degrees across the inductor