Lesson Note on Alternating Current: Capacitive Reactance, Inductive Reactance and Impedance for SS 2

Class: Senior Secondary School 2 (SS2 / SSS2)
Term: 1st Term
Week: 1
Age: 16 years
Duration: 45 minutes
Subject: Basic Electronics
Curriculum Theme: Electricity and Magnetism: Alternating Current
Previous Lesson: .
Topic: ALTERNATING CURRENT
Subject Matter: Meaning of ALTERNATING CURRENT (definition of alternating current), Concept of capacitive reactance (opposition offered by capacitor to AC), inductive reactance (opposition offered by inductor to AC), impedance (total opposition to AC in a circuit)

Specific Objectives

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

Cognitive Domain:

• Define alternating current (AC).
• Define capacitive reactance, inductive reactance, and impedance.
• State the formulas for capacitive reactance, inductive reactance, and impedance.

Affective Domain:

• Appreciate the significance of capacitive reactance, inductive reactance, and impedance in AC circuit analysis.
• Show interest in learning more about AC circuits.

Psychomotor Domain:

• Solve simple problems involving capacitive reactance and inductive reactance.
• Calculate the impedance of a basic AC circuit.

Social Domain:

• Collaborate with peers to understand complex AC concepts.
• Participate actively in class discussions.

Reference Materials

The following resources were used in planning this lesson:

• Senior Secondary Schools Education Curriculum
• State Unified Scheme of Work
• Anyakoha, M.W. (2018). New School Physics for Senior Secondary Schools. Africana First Publishers Plc.

Instructional Materials

The teacher will teach this lesson with the aid of:

• Calculator
• Resistors
• Inductors
• Capacitors
• A.C source
• Whiteboard and markers

Rationale for the Lesson

This lesson helps pupils understand how different components behave in alternating current circuits, which is fundamental to understanding modern electronics. It enables them to analyze and design simple AC circuits, a skill relevant in various technological applications.

Prerequisite/Previous Knowledge

Pupils have a basic understanding of direct current (DC) circuits, Ohm’s Law, and the functions of resistors, capacitors, and inductors.

Lesson Content/Board Summary

ALTERNATIING CURRENT (AC) CIRCUITS

Meaning of Alternating Current (AC)

Alternating current (AC) is an electric current that periodically reverses direction and continuously changes its magnitude with time, in contrast to direct current (DC), which flows only in one direction.

Capacitive Reactance (X_C)

Capacitive reactance (X_C) is the opposition offered by a capacitor to the flow of alternating current. It is measured in Ohms (Ω). Capacitive reactance decreases as the frequency of the AC or the capacitance increases.

The formula for capacitive reactance is:

X_C = 1 / (2πfC)

• X_C = Capacitive Reactance (Ohms, Ω)
• f = Frequency of the AC source (Hertz, Hz)
• C = Capacitance of the capacitor (Farads, F)
• π (pi) ≈ 3.142

Example 1: A capacitor of 20 µF is connected to an AC supply of 50 Hz. Calculate its capacitive reactance.

Step 1: Identify given values and formula.

• C = 20 µF = 20 × 10^-6 F
• f = 50 Hz
• X_C = 1 / (2πfC)

Step 2: Substitute values into the formula.

X_C = 1 / (2 × 3.142 × 50 × 20 × 10^-6)

Step 3: Calculate the result.

X_C = 1 / (0.006284)

X_C ≈ 159.15 Ω

Therefore, the capacitive reactance is approximately 159.15 Ohms.

Inductive Reactance (X_L)

Inductive reactance (X_L) is the opposition offered by an inductor to the flow of alternating current. It is measured in Ohms (Ω). Inductive reactance increases as the frequency of the AC or the inductance increases.

The formula for inductive reactance is:

X_L = 2πfL

• X_L = Inductive Reactance (Ohms, Ω)
• f = Frequency of the AC source (Hertz, Hz)
• L = Inductance of the inductor (Henries, H)
• π (pi) ≈ 3.142

Example 2: An inductor of 150 mH is connected to an AC supply of 50 Hz. Calculate its inductive reactance.

Step 1: Identify given values and formula.

• L = 150 mH = 150 × 10^-3 H
• f = 50 Hz
• X_L = 2πfL

Step 2: Substitute values into the formula.

X_L = 2 × 3.142 × 50 × 150 × 10^-3

Step 3: Calculate the result.

X_L = 47.13

X_L ≈ 47.13 Ω

Therefore, the inductive reactance is approximately 47.13 Ohms.

Impedance (Z)

Impedance (Z) is the total opposition to the flow of alternating current in an AC circuit. It is the vector sum of resistance (R), capacitive reactance (X_C), and inductive reactance (X_L). Impedance is measured in Ohms (Ω).

For a series RLC circuit, the formula for impedance is:

Z = √(R² + (X_L – X_C)²)

• Z = Impedance (Ohms, Ω)
• R = Resistance (Ohms, Ω)
• X_L = Inductive Reactance (Ohms, Ω)
• X_C = Capacitive Reactance (Ohms, Ω)

Example 3: A series circuit has a resistor of 100 Ω, an inductor with an inductive reactance of 40 Ω, and a capacitor with a capacitive reactance of 60 Ω. Calculate the total impedance of the circuit.

Step 1: Identify given values and formula.

• R = 100 Ω
• X_L = 40 Ω
• X_C = 60 Ω
• Z = √(R² + (X_L – X_C)² )

Step 2: Substitute values into the formula.

Z = √(100² + (40 – 60)²)

Z = √(100² + (-20)²)

Z = √(10000 + 400)

Z = √(10400)

Step 3: Calculate the result.

Z ≈ 101.98 Ω

Therefore, the total impedance of the circuit is approximately 101.98 Ohms.

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 reminds them about direct current (DC) and how it flows in one direction. The teacher then introduces alternating current (AC) as current that changes direction periodically.
Pupils’ Activity: Pupils respond to greetings and recall their knowledge of DC, then listen attentively to the introduction of AC.
Learning Point: Pupils are introduced to the concept of alternating current and its contrast with direct current.

Step 2: Meaning of Alternating Current

Time: 5 minutes
Teaching Skill: Explanation
Teacher’s Activity: The teacher defines alternating current (AC) and explains its characteristics, such as periodic reversal of direction and continuous change in magnitude.
Pupils’ Activity: Pupils listen, ask questions for clarification, and copy the definition into their notes.
Learning Point: Pupils understand the fundamental definition and characteristics of alternating current.

Step 3: Capacitive Reactance

Time: 7 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher explains the concept of capacitive reactance (X_C) as the opposition offered by a capacitor to AC, states its formula, and solves Example 1 on the board.
Pupils’ Activity: Pupils listen, observe the demonstration (if any), copy the formula and example, and ask questions.
Learning Point: Pupils understand capacitive reactance, its formula, and how to calculate it.

Step 4: Inductive Reactance

Time: 7 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher explains inductive reactance (X_L) as the opposition offered by an inductor to AC, states its formula, and solves Example 2 on the board.
Pupils’ Activity: Pupils listen, observe, copy the formula and example, and participate in discussion.
Learning Point: Pupils understand inductive reactance, its formula, and how to calculate it.

Step 5: Impedance

Time: 8 minutes
Teaching Skill: Explanation/Problem Solving
Teacher’s Activity: The teacher defines impedance (Z) as the total opposition to AC in a circuit, presents the formula for a series RLC circuit, and solves Example 3 on the board.
Pupils’ Activity: Pupils pay attention, copy the definition, formula, and example, and attempt to solve along with the teacher.
Learning Point: Pupils understand impedance, its formula, and how to calculate it for a series RLC circuit.

Step 6: Class Work/Practice

Time: 5 minutes
Teaching Skill: Guided Practice
Teacher’s Activity: The teacher provides a short practice problem for pupils to solve individually or in pairs, assisting where needed.
Pupils’ Activity: Pupils attempt to solve the practice problem based on the concepts taught.
Learning Point: Pupils apply their knowledge to solve problems and reinforce their understanding.

Step 7: Evaluation/Review

Time: 5 minutes
Teaching Skill: Questioning/Assessment
Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. Define alternating current.
2. What is capacitive reactance? State its formula.
3. What is inductive reactance? State its formula.
4. Define impedance and state its formula for a series RLC circuit.
5. Calculate the capacitive reactance of a 10 µF capacitor connected to a 100 Hz AC source.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 3 minutes
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarizes the key learning points on alternating current, capacitive reactance, inductive reactance, and impedance. The teacher then gives homework, asking pupils to find real-life applications of AC circuits.
Pupils’ Activity: Pupils listen to the summary and copy down the homework assignment.
Learning Point: Pupils consolidate their understanding and are encouraged to research further.

Lesson Keywords

• Alternating Current (AC) – Electric current that periodically reverses direction.
• Capacitive Reactance (X_C) – Opposition to AC flow by a capacitor.
• Inductive Reactance (X_L) – Opposition to AC flow by an inductor.
• Impedance (Z) – Total opposition to AC flow in a circuit.

Differentiation

For pupils who grasp concepts quickly, the teacher can provide more complex problems involving phase angles or resonance. For pupils needing more support, the teacher will offer simplified examples, provide one-on-one guidance, and encourage peer tutoring.

Note for teachers using this lesson plan

Ensure that pupils have a solid understanding of basic electrical terms and units before starting this lesson. Emphasize the practical implications of these concepts in everyday electronics. Encourage the use of calculators for computations. If possible, use real components (resistors, capacitors, inductors) and a signal generator to demonstrate the effect of varying frequency.