AS

310102jB Fundamentals of Alternating Current Part B 2025 (TF)

Fundamentals of Alternating Current - Part B

Objectives

  • Describe the factors affecting impedance in an AC circuit.

Resistive Loads

  • Definition of an AC circuit with resistors in series.

  • In a series circuit:

    • Total Impedance = Resistance (No Reactance exists).

Phasors in Series Resistor Circuits

  • Current Reference: In a series circuit, current remains constant throughout.

  • Phasor diagrams for individual resistors (Resistor 1, Resistor 2, Resistor 3) show phase relationships.

Adding Voltage Drops in Resistive Circuits

  • Voltage drops can be added normally in purely resistive circuits because:

    • Voltage and current are in-phase.

    • Only horizontal components exist in phasors, no vertical components.

Voltage and Current Waves

  • Waveforms:

    • Voltage wave and current wave shown in relation to time.

    • Key phases: 0°, 90°, 180°, 270°, and 360°.

Example Resistor Circuit

  • Example calculation of voltage across resistors (Examples include VR₁ = 10 V, VR₃ = 6 V).

  • Application of Kirchhoff's Voltage Law for finding voltage drops.

Phase Relationships in Series Circuits

  • No phase angle or shift between voltage and current; they are in-phase.

  • Phasor diagrams illustrate this relationship.

Self-Induction in Coils

  • Induction occurs due to changing current in a coil which induces an emf across adjacent turns due to changing flux.

Inductors in Series

  • Total inductance of inductors in series is the sum of individual inductances:

    • Example: L₁ = 0.16 H, L₂ = 0.2 H, yielding LT = 0.36 H.

Voltage and Current Relationships in Inductive Circuits

  • In a purely inductive circuit:

    • Current lags voltage by 90°.

    • Phasor representations show voltage leading current.

Capacitive Circuits

  • Capacitors in Series:

    • Designated values (example: C1 = 265Ω, C2 = 53.05Ω).

    • As capacitors are added, the distance between plates increases, resulting in decreased capacitance.

Capacitive Reactance

  • Combination of capacitors in series leads to an additive effect on capacitive reactance (Xc).

Voltage Drops in Capacitors

  • Voltage across capacitors is in phase but lags current by 90°.

Impedance in AC Circuits

  • Impedance limits current similar to resistance in DC circuits, and is affected by:

    • Inductive Reactance (X).

    • Capacitive Reactance (Xc).

    • Overall impedance is a combination of resistance, inductance, and capacitance.

AC Series RLC Circuits

  • Analysis of Series RLC Circuits:

    • R, XL, and XC must be summed to determine total Z (impedance).

    • Resonant frequency occurs when XL equals XC, causing them to cancel out.

Resultant Reactance

  • Determination of resultant reactance based on differing values of XL and XC; impacts circuit behavior.

  • Visually represented in impedance triangles showing phase relationships of voltage and current.

Practical Application

  • Analyze circuits using values presented in example problems for better understanding of underlying principles.