Lesson Note on Alternating Current: Calculation of Series Resonance and Parallel Resonance for SS 2

Class: Senior Secondary School 2 (SS2 / SSS2)
Term: 1st Term
Week: 5
Age: 16 years
Duration: 45 minutes
Subject: Basic Electronics
Curriculum Theme: Electrical Circuits
Previous Lesson: RLC Circuits.
Topic: ALTERNATING CURRENT
Subject Matter: Meaning of ALTERNATING CURRENT, calculation of series resonance, calculation of parallel resonance.

Specific Objectives

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

Cognitive Domain:

• Define alternating current (AC).
• State the formula for series resonance frequency.
• State the formula for parallel resonance frequency.

Affective Domain:

• Appreciate the importance of resonance in electronic circuits.
• Show interest in solving problems related to resonance.

Psychomotor Domain:

• Calculate the resonance frequency for a series RLC circuit given component values.
• Calculate the resonance frequency for a parallel RLC circuit given component values.

Social Domain:

• Collaborate with peers to solve resonance problems.

Reference Materials

The following resources were used in planning this lesson:

• Senior Secondary Schools Education Curriculum
• State Unified Scheme of Work
• NELSON THORNES, Basic Electronics for Senior Secondary Schools.
• https://www.allaboutcircuits.com/textbook/alternating-current/chpt-6/series-resonance/
• https://www.electronics-tutorials.ws/accircuits/parallel-resonance.html

Instructional Materials

The teacher will teach this lesson with the aid of:

• Calculators
• Circuit diagrams of series and parallel RLC circuits
• Whiteboard and markers
• Textbooks

Rationale for the Lesson

Understanding alternating current and resonance is important for pupils to grasp how many electronic devices work. This lesson helps pupils to analyze and design circuits used in radios, filters, and communication systems.

Prerequisite/Previous Knowledge

Pupils are expected to have a basic understanding of alternating current (AC), capacitors, inductors, resistors, and RLC circuits.

Lesson Content/Board Summary

ALTERNATING CURRENT AND RESONANCE

Meaning of Alternating Current (AC)

Alternating current (AC) is an electric current which periodically reverses direction, in contrast to direct current (DC) which flows only in one direction. AC is the form in which electric power is delivered to businesses and residences.

Series Resonance

Series resonance occurs in an RLC series circuit when the inductive reactance (X_L) becomes equal to the capacitive reactance (X_C). At this point, the impedance of the circuit is at its minimum, and the current is at its maximum.

The formula for the series resonance frequency (f_r) is:

f_r = 1 / (2π√(LC))

Where:

• f_r = Resonance frequency in Hertz (Hz)
• L = Inductance in Henrys (H)
• C = Capacitance in Farads (F)
• π ≈ 3.142

Worked Example 1 (Series Resonance):

A series RLC circuit has an inductor of 10 mH and a capacitor of 0.1 μF. Calculate the resonance frequency.

Step 1: Identify given values and convert to standard units.

• L = 10 mH = 10 × 10^-3 H
• C = 0.1 μF = 0.1 × 10^-6 F = 1 × 10^-7 F

Step 2: Apply the series resonance formula.

f_r = 1 / (2π√(LC))

f_r = 1 / (2 × 3.142 × √((10 × 10^-3) × (1 × 10^-7)))

f_r = 1 / (2 × 3.142 × √(1 × 10^-9))

f_r = 1 / (2 × 3.142 × 3.162 × 10^-5)

f_r = 1 / (1.987 × 10^-4)

f_r ≈ 5032 Hz or 5.032 kHz

Worked Example 2 (Series Resonance):

Find the resonance frequency of a series circuit with L = 50 mH and C = 20 nF.

Step 1: Identify given values and convert to standard units.

• L = 50 mH = 50 × 10^-3 H
• C = 20 nF = 20 × 10^-9 F

Step 2: Apply the series resonance formula.

f_r = 1 / (2π√(LC))

f_r = 1 / (2 × 3.142 × √((50 × 10^-3) × (20 × 10^-9)))

f_r = 1 / (2 × 3.142 × √(1000 × 10^-12))

f_r = 1 / (2 × 3.142 × √(1 × 10^-9))

f_r = 1 / (2 × 3.142 × 3.162 × 10^-5)

f_r = 1 / (1.987 × 10^-4)

f_r ≈ 5032 Hz or 5.032 kHz

Parallel Resonance

Parallel resonance occurs in an RLC parallel circuit when the inductive reactance (X_L) equals the capacitive reactance (X_C). At this point, the impedance of the circuit is at its maximum, and the current drawn from the supply is at its minimum.

The formula for the parallel resonance frequency (f_p) is the same as for series resonance:

f_p = 1 / (2π√(LC))

Where:

• f_p = Resonance frequency in Hertz (Hz)
• L = Inductance in Henrys (H)
• C = Capacitance in Farads (F)
• π ≈ 3.142

NOTE: For a parallel RLC circuit, the resonance frequency formula is identical to that of a series RLC circuit, assuming ideal components.

Worked Example 1 (Parallel Resonance):

A parallel RLC circuit has an inductor of 20 mH and a capacitor of 0.05 μF. Calculate the resonance frequency.

Step 1: Identify given values and convert to standard units.

• L = 20 mH = 20 × 10^-3 H
• C = 0.05 μF = 0.05 × 10^-6 F = 5 × 10^-8 F

Step 2: Apply the parallel resonance formula.

f_p = 1 / (2π√(LC))

f_p = 1 / (2 × 3.142 × √((20 × 10^-3) × (5 × 10^-8)))

f_p = 1 / (2 × 3.142 × √(100 × 10^-11))

f_p = 1 / (2 × 3.142 × √(1 × 10^-9))

f_p = 1 / (2 × 3.142 × 3.162 × 10^-5)

f_p = 1 / (1.987 × 10^-4)

f_p ≈ 5032 Hz or 5.032 kHz

Worked Example 2 (Parallel Resonance):

Determine the resonance frequency for a parallel circuit with L = 100 mH and C = 10 nF.

Step 1: Identify given values and convert to standard units.

• L = 100 mH = 100 × 10^-3 H = 0.1 H
• C = 10 nF = 10 × 10^-9 F

Step 2: Apply the parallel resonance formula.

f_p = 1 / (2π√(LC))

f_p = 1 / (2 × 3.142 × √((0.1) × (10 × 10^-9)))

f_p = 1 / (2 × 3.142 × √(1 × 10^-9))

f_p = 1 / (2 × 3.142 × 3.162 × 10^-5)

f_p = 1 / (1.987 × 10^-4)

f_p ≈ 5032 Hz or 5.032 kHz

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 to recall what they learned about alternating current (AC) and RLC circuits in the previous lesson.
Pupils’ Activity: Pupils respond to the teacher’s questions, recalling previous knowledge.
Learning Point: Pupils activate prior knowledge related to AC and RLC circuits.

Step 2: Meaning of Alternating Current (AC)

Time: 5 minutes
Teaching Skill: Explanation/Recap
Teacher’s Activity: The teacher recaps the meaning of alternating current, emphasizing its characteristics and common applications.
Pupils’ Activity: Pupils listen attentively and contribute by stating examples of AC applications.
Learning Point: Pupils solidify their understanding of alternating current.

Step 3: Concept of Series Resonance

Time: 7 minutes
Teaching Skill: Explanation/Illustration
Teacher’s Activity: The teacher introduces the concept of series resonance, explaining how it occurs in an RLC circuit and its effect on impedance and current. The teacher writes the formula on the board.
Pupils’ Activity: Pupils listen, take notes, and ask clarifying questions about the concept.
Learning Point: Pupils understand the conditions and formula for series resonance.

Step 4: Calculation of Series Resonance (Example 1)

Time: 8 minutes
Teaching Skill: Demonstration/Problem Solving
Teacher’s Activity: The teacher demonstrates the first worked example of calculating series resonance frequency on the board, showing each step clearly.
Pupils’ Activity: Pupils observe carefully, copy the example into their notes, and ensure they understand the calculations.
Learning Point: Pupils learn the step-by-step process of calculating series resonance.

Step 5: Calculation of Series Resonance (Example 2)

Time: 5 minutes
Teaching Skill: Guided Practice
Teacher’s Activity: The teacher provides a second example for series resonance and guides pupils to solve it individually or in pairs.
Pupils’ Activity: Pupils attempt to solve the problem, seeking assistance from the teacher when needed.
Learning Point: Pupils practice applying the series resonance formula.

Step 6: Concept and Calculation of Parallel Resonance (Example 1)

Time: 8 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher explains the concept of parallel resonance, its characteristics, and states that the formula for resonance frequency is the same as for series resonance. The teacher then demonstrates the first worked example for parallel resonance.
Pupils’ Activity: Pupils listen, take notes, and follow the demonstration of the parallel resonance calculation.
Learning Point: Pupils understand parallel resonance and its calculation.

Step 7: Calculation of Parallel Resonance (Example 2) and Evaluation/Review

Time: 5 minutes
Teaching Skill: Questioning/Assessment
Teacher’s Activity: The teacher provides a second example for parallel resonance for pupils to solve. The teacher evaluates the learning by asking the following questions:

1. What is alternating current (AC)?
2. State the formula for calculating series resonance frequency.
3. Explain what happens to circuit impedance at series resonance.
4. Calculate the resonance frequency of a parallel circuit with L = 25 mH and C = 0.2 μF.

Pupils’ Activity: Pupils answer orally and in writing.
Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 2 minutes
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the importance of resonance in AC circuits.
Pupils’ Activity: Pupils listen and ask any remaining questions.
Learning Point: Pupils consolidate their learning.

Lesson Keywords

• Alternating Current (AC) – Electric current that periodically reverses direction.
• Resonance – A phenomenon in RLC circuits where inductive and capacitive reactances cancel each other.
• Series Resonance – Occurs in a series RLC circuit when X_L = X_C, leading to minimum impedance and maximum current.
• Parallel Resonance – Occurs in a parallel RLC circuit when X_L = X_C, leading to maximum impedance and minimum current.
• Inductance (L) – The property of an electrical conductor to oppose a change in the electric current flowing through it.
• Capacitance (C) – The ability of a system to store an electric charge.
• Resonance Frequency (f_r) – The specific frequency at which resonance occurs.

Differentiation

For pupils who grasp the concepts quickly, the teacher can provide more complex problems involving quality factor (Q-factor) or bandwidth. For pupils who need more support, the teacher will provide simplified examples and one-on-one guidance, possibly using visual aids to explain the concepts of reactance cancellation.

Note for teachers using this lesson plan

Ensure pupils understand the difference between series and parallel resonance in terms of impedance and current behavior, even though the frequency formula is the same. Emphasize the importance of correct unit conversion before calculations. Encourage pupils to use their calculators efficiently.