Class: Senior Secondary School 2 (SS2 / SSS 2)
Term: 1st Term
Week: 6
Age: 16 years
Duration: 45 minutes
Subject: Basic Electronics
Curriculum Theme: Electrical Power and Circuits
Previous Lesson: Alternating Current: Calculation of Series Resonance and Parallel Resonance.
Topic: POWER IN AC CIRCUIT.
Subject Matter: Meaning of POWER IN AC CIRCUIT (definition of power in AC circuit), power (real power in AC), power triangle (relationship of real reactive apparent power), power factor (cosine of phase angle), power factor correction (methods to improve power factor).

Specific Objectives

By the end of the lesson, pupils should be able to:

Cognitive Domain:

Define power in an AC circuit.
Explain the three types of power in AC circuits: real, reactive, and apparent power.
State the relationship between real, reactive, and apparent power using the power triangle.
Define power factor and state its formula.
List methods used for power factor correction.

Affective Domain:

Appreciate the importance of power factor correction in electrical systems.
Value the efficient use of electrical power.

Psychomotor Domain:

Draw a power triangle showing the relationship between different types of power.
Calculate the power factor given real and apparent power or phase angle.

Collaborate with peers to discuss the implications of low power factor.

Reference Materials

The following resources were used in planning this lesson:

Senior Secondary Schools Education Curriculum
State Unified Scheme of Work
Theraja, B. L., & Theraja, A. K. (2010). A Textbook of Electrical Technology, Vol. 1 & 2. S. Chand & Company Ltd.
https://www.electrical4u.com/power-in-ac-circuit/
https://www.electronics-tutorials.ws/accircuits/ac-power.html

Instructional Materials

The teacher will teach this lesson with the aid of:

Charts on power triangle
Whiteboard and markers
Calculator

Rationale for the Lesson

Understanding power in AC circuits is important for pupils to grasp how electrical energy is consumed and managed in homes and industries. This lesson helps pupils understand concepts like efficiency and cost-effectiveness in electrical systems, which are relevant in daily life and future careers.

Prerequisite/Previous Knowledge

Pupils should have prior knowledge of basic AC circuit concepts, including voltage, current, resistance, impedance, and phase difference.

Lesson Content/Board Summary

POWER IN AC CIRCUIT

1. Definition of Power in AC Circuit

Power in an AC circuit refers to the rate at which electrical energy is transferred or consumed by the circuit components. Unlike DC circuits, AC circuits have three types of power due to the phase difference between voltage and current.

2. Types of Power in AC Circuits

The three types of power in AC circuits are:

Real Power (P): Also known as active power or true power, it is the actual power dissipated by the circuit’s resistance and does useful work. It is measured in watts (W).
Reactive Power (Q): This is the power exchanged between the source and the reactive components (inductors and capacitors) of the circuit. It does not perform useful work but is necessary for the operation of reactive loads. It is measured in volt-ampere reactive (VAR).
Apparent Power (S): This is the total power delivered by the source, which is the vector sum of real and reactive power. It is the product of the RMS voltage and RMS current. It is measured in volt-amperes (VA).

3. Power Triangle

The power triangle illustrates the relationship between real power (P), reactive power (Q), and apparent power (S). It is a right-angled triangle where:

The adjacent side represents Real Power (P).
The opposite side represents Reactive Power (Q).
The hypotenuse represents Apparent Power (S).
The angle (φ) between the apparent power and real power is the phase angle.

Relationship: S² = P² + Q²

4. Power Factor (PF)

Power factor is the cosine of the phase angle (φ) between the voltage and current in an AC circuit. It is also the ratio of real power to apparent power.

Formula: PF = cos(φ) = P / S

A power factor close to 1 (unity) indicates efficient use of power, while a low power factor indicates poor efficiency.

5. Power Factor Correction

Power factor correction is the process of improving the power factor of an AC circuit, usually by reducing the phase difference between voltage and current. This is done to increase efficiency and reduce electricity costs.

6. Methods to Improve Power Factor

Common methods for power factor correction include:

Using Capacitors: Capacitors draw leading reactive power, which compensates for the lagging reactive power drawn by inductive loads (motors, transformers).
Using Synchronous Condensers: These are over-excited synchronous motors operating without mechanical load, drawing leading reactive power.
Using Static VAR Compensators (SVCs): Electronic devices that can rapidly adjust reactive power output.

Worked Example: Calculating Power Factor

Example 1: An AC circuit has a real power of 1200 W and an apparent power of 1500 VA. Calculate the power factor.

Step 1: Identify given values.

Real Power (P) = 1200 W
Apparent Power (S) = 1500 VA

Step 2: Apply the power factor formula.

PF = P / S

PF = 1200 W / 1500 VA

Step 3: Calculate the power factor.

PF = 0.8

The power factor is 0.8 (often lagging for typical industrial loads).

Example 2: An inductive load draws 10A at 240V, with a phase angle of 36.87° between voltage and current. Calculate the power factor and apparent power.

Step 1: Identify given values.

Voltage (V) = 240 V
Current (I) = 10 A
Phase angle (φ) = 36.87°

Step 2: Calculate the power factor.

PF = cos(φ)

PF = cos(36.87°)

PF ≈ 0.8

Step 3: Calculate apparent power.

S = V × I

S = 240 V × 10 A

S = 2400 VA

The power factor is approximately 0.8, and the apparent power is 2400 VA.

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher greets the pupils and asks them what they understand by power in DC circuits to link to AC circuits.
Pupils’ Activity: Pupils respond by defining power in DC circuits.
Learning Point: Pupils recall previous knowledge on power.

Step 2: Meaning of Power in AC Circuit and Real Power

Time: 8 minutes
Teaching Skill: Explanation/Definition
Teacher’s Activity: The teacher explains the concept of power in AC circuits, focusing on real power and its unit (Watts).
Pupils’ Activity: Pupils listen attentively and take notes.
Learning Point: Pupils understand the definition of power in AC circuits and real power.

Step 3: Power Triangle and Other Types of Power

Time: 10 minutes
Teaching Skill: Illustration/Explanation
Teacher’s Activity: The teacher uses a chart to explain the power triangle, defining reactive power (VAR) and apparent power (VA), and their relationship (S² = P² + Q²).
Pupils’ Activity: Pupils observe the chart, ask questions, and copy the power triangle.
Learning Point: Pupils understand the relationship between real, reactive, and apparent power.

Step 4: Power Factor

Time: 7 minutes
Teaching Skill: Definition/Formula
Teacher’s Activity: The teacher defines power factor as the cosine of the phase angle and the ratio of real power to apparent power (PF = cos φ = P/S), explaining its significance.
Pupils’ Activity: Pupils listen, take notes, and ask questions for clarity.
Learning Point: Pupils understand the definition and formula for power factor.

Step 5: Need for Power Factor Correction

Time: 5 minutes
Teaching Skill: Explanation
Teacher’s Activity: The teacher explains why power factor correction is needed (e.g., to reduce energy losses, improve voltage regulation, reduce electricity bills).
Pupils’ Activity: Pupils listen and contribute to the discussion on the importance of power factor.
Learning Point: Pupils understand the reasons for improving power factor.

Step 6: Methods of Power Factor Correction

Time: 5 minutes
Teaching Skill: Listing/Explanation
Teacher’s Activity: The teacher explains various methods used to improve power factor, such as using capacitors and synchronous condensers.
Pupils’ Activity: Pupils note down the methods of power factor correction.
Learning Point: Pupils identify different techniques for power factor improvement.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

Define power in an AC circuit.
State the three types of power in AC circuits and their units.
Draw a power triangle and state the relationship between real, reactive, and apparent power.
Calculate the power factor if the real power is 1000 W and the apparent power is 1250 VA.
Mention two methods of power factor correction.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 5 minutes
Teaching Skill: Summarization/Assignment
Teacher’s Activity: The teacher summarizes the key points of the lesson and gives pupils an assignment to research practical applications of power factor correction in industries.
Pupils’ Activity: Pupils copy the assignment.
Learning Point: Pupils reinforce their understanding and are encouraged to research further.

Lesson Keywords

Real Power – The actual power consumed by the circuit, measured in Watts.
Reactive Power – Power exchanged between source and reactive components, measured in VAR.
Apparent Power – Total power delivered by the source, measured in VA.
Power Triangle – A right-angled triangle showing the relationship between real, reactive, and apparent power.
Power Factor – The cosine of the phase angle between voltage and current, or the ratio of real power to apparent power.
Power Factor Correction – Methods used to improve the power factor of an AC circuit.

Differentiation

For pupils who grasp concepts quickly, the teacher can provide more complex calculation problems involving impedance and phase angles. For pupils needing more support, the teacher will focus on defining terms and illustrating the power triangle with simple examples, providing additional one-on-one guidance.

Note for teachers using this lesson plan

Ensure that pupils clearly understand the difference between real, reactive, and apparent power as this is fundamental to understanding power factor. Emphasize the practical implications of low power factor and the benefits of correction. Encourage pupils to draw and label the power triangle accurately.