Definitive Study Notes on Electrical Components and Systems

Learning Resource: Knowledge of Capacitors, Inductance, Power Factor, and Power Factor Correction

Trainee Information

• Name: _____________________________________________________________________

• Electrical Apprenticeship: 29476v2 – v4.0

• Training Company: The Electrical Training Company

Table of Contents

1. Part 1: Introduction to Capacitors

   • 1.1 Construction of a Capacitor

   • 1.2 Capacitor Types

   • 1.3 Charging a Capacitor

   • 1.4 Discharging a Capacitor

   • 1.5 Capacitance

   • 1.6 Factors Affecting Capacitance

   • 1.7 Connecting Capacitors in a Circuit

     • 1.7.1 The Series Connection

     • 1.7.2 Capacitor Voltage in Series

     • 1.7.3 Capacitors in Parallel

     • 1.7.4 Capacitor Voltage in Parallel

   • 1.8 Capacitor Markings

   • 1.9 Regulatory Requirements and Safety Precautions

   • 1.10 Radio Interference Suppression

   • 1.11 Applications of Capacitors

   • 1.12 Power Factor Correction

   • 1.13 Reduction of Arcing

   • 1.14 Voltage Control

2. Part 2: Introduction to Inductors

   • 2.1 Inductor Construction

   • 2.2 Inductive Fields

   • 2.3 Inductor Materials

   • 2.4 Applications of Inductors

     • 2.4.1 Applications in AC Circuits

     • 2.4.2 Autotransformers

     • 2.4.3 Variacs

     • 2.4.4 AC Arc Welders

   • 2.5 Power Factor Correction Applications

   • 2.6 Inductive Discharging

3. Part 3: Vector and Phasor Quantities

   • 3.1 Scalar Quantities

   • 3.2 Vector Quantities

   • 3.3 Vectors Acting in a Straight Line

   • 3.4 Vectors Acting at Angles Other than 90°

   • 3.5 Parallelogram Method

   • 3.6 Polygon Method

   • 3.7 Trigonometric Method

   • 3.8 Phasors

   • 3.9 Adding Phasors at Different Angles

   • 3.10 Adding Phasors by Calculation

   • 3.11 Adding Phasors Using Complex Numbers

4. Part 4: Reactive Components and Power in AC Circuits

   • 4.1 AC Ohms Law

   • 4.2 Reactance

   • 4.3 Circuit Impedance

   • 4.4 RC Circuit Impedance

   • 4.5 RL Circuit Impedance

   • 4.6 Voltage Drop across Components

5. Part 5: Inductance and Capacitance in AC Circuits

   • 5.1 Circuit Impedance Examples

   • 5.2 Phase Relationships

6. Part 6: Electrical Power and Energy

   • 6.1 Electrical Power Defined

   • 6.2 Power Formulas

   • 6.3 Power Calculations

   • 6.4 Cost Calculation for Electrical Use

7. Part 7: AC Power Factor

   • 7.1 Resistive Power

   • 7.2 Reactive Power

   • 7.3 Apparent Power

   • 7.4 Power Triangle

   • 7.5 Effects of Low Power Factor

   • 7.6 Correcting Power Factor

8. Part 8: Correcting Lagging Power Factor

   • 8.1 Calculating Power Factor Correction Capacitor Values

   • 8.2 Determining Corrective VAR

   • 8.3 Calculating Required Supply Current

Part 1: Introduction to Capacitors

1.1 Construction of a Capacitor

• Capacitance: Ability of a component to collect and store energy in the form of an electrical charge.

• Basic Structure: Two or more parallel metal plates (conductors) separated by an insulating layer (dielectric).

• Dielectric Materials: Air, waxed paper, mica, plastic, ceramic.

1.2 Capacitor Types

1. Fixed Capacitors:

   • Polarised Capacitors: Used in DC applications; sensitive to connection polarity.

     • Marking: Positive plate must connect to the positive terminal and the negative plate to the negative terminal.

   • Non-Polarised Capacitors: Can be used in AC and DC applications.

2. Variable Capacitors: Can change capacitance by adjusting plate area or distance.

1.3 Charging a Capacitor

• Mechanism:

  • External voltage source moves electrons from one plate (positive charge) to another (negative charge).

  • Induced Separation: Causes stress in dielectric material, allowing the capacitor to store charge until supply voltage equals voltage across capacitor plates.

  • Charging Cycle: High initial current, reducing as charge builds up and voltage equalizes.

• Safety Compliance: Capacitors above 0.5 µF must have a discharge path per AS/NZS 3000.

1.4 Discharging a Capacitor

• Connect plates with conductive path (e.g., wire) to allow electrons to flow and equalize charge.

• Caution: High initial current can occur; adequate resistance recommended for discharge paths.

1.5 Capacitance

• Definition: Amount of energy a capacitor can store; measured in Farads (F).

• Calculation Formula: $C = rac{Q}{V}$

  • Where:

    • $C$: Capacitance (F)

    • $Q$: Charge (C)

    • $V$: Voltage (V)

• Common Values: Microfarads (µF), Nanofarads (nF), Picofarads (pF).

1.6 Factors Affecting Capacitance

• Directly Proportional:

  • Area of the plates.

• Inversely Proportional:

  • Distance between the plates.

• Dielectric Type: Affects the overall capacitance value.

1.7 Connecting Capacitors in a Circuit

• Series Connections:

  • Increase effective plate separation, reducing capacitance.

  • Calculation Formula: $rac{1}{C_t} = rac{1}{C_1} + rac{1}{C_2} + rac{1}{C_3}$

  • Example: For capacitors 3.0 µF and 5.0 µF connected in series:

    • $rac{1}{C_t} = rac{1}{3} + rac{1}{5} = rac{1}{1.875} <br>ightarrow C_t = 1.875 µF$

1.8 Capacitor Voltage in Series

• Voltage across capacitors

  • Inversely proportional to capacitance: smallest capacitance has highest voltage.

1.9 Capacitors in Parallel

• Total Capacitance Calculation:

  • $C_t = C_1 + C_2 + C_3$

  • Example: Two capacitors 3.0 µF and 5.0 µF give:

    • $C_t = 3 + 5 = 8 µF$

• Voltage across capacitors in parallel: All capacitors have same supply voltage.

1.10 Capacitor Markings

• Different marking systems exist; flow from type and technology used.

• Example IEC Code:

  • 1 is numeral, 8 is numeral, 4 is the multiplier, J is tolerance, and 50 is working voltage.

1.11 Regulatory Requirements and Safety Precautions

• Capacitors block DC and allow AC; store energy and draw current leading voltage.

• Safety Precautions:

  • Discharge capacitors before handling; use resistor, check insulation, and follow AS/NZS 3000.

1.12 Radio Interference Suppression

• Sparking at brush motors can cause radio interference; suppress by connecting capacitors in parallel.

• Capacitors for interference must be rated for at least 500V AC and not larger than 0.005 μF.

1.13 Applications of Capacitors

• Electronic Coupling: Used in amplifiers to block DC signals.

• Smoothing: Reduces ripple in rectifier outputs.

• Contact Protection: Reduces arcing at switch contacts.

1.14 Power Factor Correction

• Improves efficiency by reducing reactive power.

• Components designed to correct inductive loads with capacitors.

1.15 Reduction of Arcing

• Arcing during switch operations can be reduced using capacitors as snubbers, minimizing wear and EMI.

• Voltage Control: Series capacitor banks can stabilize voltage in distribution systems.

Part 2: Introduction to Inductors

2.1 Inductor Construction

• Inductors generate magnetic fields when electrical current flows through them, storing energy.

• Components: A coil of insulated wire, often around a ferromagnetic core.

2.2 Inductive Fields

• Inductors convert electrical energy to magnetic energy, oppose changes in current, and can create self-induction.

• Self-Induction: Induces an EMF that opposes current changes due to the changing magnetic field.

2.3 Inductor Materials

• Common core materials include air-cored (non-magnetic), iron-cored (laminated), and ferrite-cored (ceramic). Each affects inductive properties uniquely.

2.4 Applications of Inductors

• Chokes: Used in circuits for current limiting.

• Transformers: Change AC voltage levels and provide isolation.

2.5 Power Factor Correction Applications

• Inductive loads can create a lagging power factor, needing correction with capacitors.

2.6 Inductive Discharging

• During circuit opening, stored energy can cause inductive transients (high voltage spikes).

Part 3: Vector and Phasor Quantities

3.1 Scalar Quantities

• Defined by magnitude only: e.g., energy, length, volume.

3.2 Vector Quantities

• Defined by both magnitude and direction: e.g., force, current.

3.3 Vectors Acting in a Straight Line

• Represented by arrows where length is magnitude.

3.4 Vectors Acting at Angles Other than 90°

• Utilize methods like the parallelogram and trigonometric methods to resolve vectors.

3.5 Parallelogram Method

• Allows for graphical addition of two vectors using scale and protractor.

3.6 Polygon Method

• For multiple vectors, follow the same steps as the parallelogram method, tracing resulting vector with accurate angles.

3.7 Trigonometric Method

• Utilizes right triangles to calculate vector components.

3.8 Phasors

• Represent time-varying quantities in AC circuits with both direction and length.

3.9 Adding Phasors at Different Angles

• Described using graphical means and calculations to derive resultant phasor.

3.10 Adding Phasors by Calculation

• Using trigonometry and complex number methods to determine resultant values.

Part 4: Reactive Components and Power in AC Circuits

4.1 AC Ohms Law

• Ohm’s Law adapts for AC to accommodate phase differences, requiring the use of impedance instead of resistance.

4.2 Reactance

• The opposition to changes in current in reactive components; includes inductive and capacitive reactance.

4.3 Circuit Impedance

• Total opposition (Z) combines resistance and reactance; measured in ohms.

4.4 RC Circuit Impedance

• Uses Pythagorean theorem to determine impedance that combines resistive and capacitive elements.

4.5 RL Circuit Impedance

• Similar to RC, combining inductive reactance into total impedance calculations.

4.6 Voltage Drop across Components

• Illustrates how voltage is distributed across components based on their impedances.

Part 5: Inductance and Capacitance in AC Circuits

5.1 Circuit Impedance Examples

• Various examples providing calculations of impedance for circuits with inductors and capacitors.

5.2 Phase Relationships

• The phase relationships between voltage and current in reactive and resistive circuits can affect energy usage and component durability.

Part 6: Electrical Power and Energy

6.1 Electrical Power Defined

• Power conveys the rate of work done; measured in watts (W).

6.2 Power Formulas

• Relate voltage, current, resistance and work with applicable formulas.

6.3 Power Calculations

• Explained discovery of electrical power from voltage and current relationships, addressing reactive constituents.

6.4 Cost Calculation for Electrical Use

• Outlines understanding of energy consumption costs and their calculation from power usage.

Part 7: AC Power Factor

7.1 Resistive Power

• Defined as the power that dissipates without phase lag.

7.2 Reactive Power

• Power attributed to storage in inductors and capacitors with a character of leading or lagging based on circuit components.

7.3 Apparent Power

• The total power calculated from voltage and current; does not reflect usable power when reactance exists.

7.4 Power Triangle

• Visualizes relationships of active power, reactive power and apparent power to understand AC circuits effectively.

7.5 Effects of Low Power Factor

• Addresses the outcomes of a low power factor on the efficiency of installations, viability needs, and additional costs associated.

7.6 Correcting Power Factor

• Discusses methods to alleviate issues caused by inductive loads, including the strategic application of capacitors.

Part 8: Correcting Lagging Power Factor

8.1 Calculating Power Factor Correction Capacitor Values

• Outlines calculations for determining necessary capacitor values required to correct power factors.

8.2 Determining Corrective VAR

• Analyze how reactive power equations interlink with load and phase shift adjustments.

8.3 Calculating Required Supply Current

• Provides methods to determine the impact of varying power factors on the supply current required to sustain operational requirements