Class: Senior Secondary School 2 (SS2 / SSS2)
Term: 1st Term
Week: 8
Age: 16 years
Duration: 45 minutes
Subject: Basic Electricity
Curriculum Theme: Electrical Machines
Previous Lesson: DC Generators: Meaning, Induced EMF and Main Parts.
Topic: DC GENERATOR
Subject Matter: Calculation of generated voltage (EMF computation), output voltage (terminal voltage determination)

Specific Objectives

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

Cognitive Domain:

Define generated electromotive force (EMF) and terminal voltage.
State the formulas for calculating generated EMF and terminal voltage.
Explain the factors affecting the magnitude of generated EMF.

Affective Domain:

Appreciate the importance of accurately calculating voltages in DC generators.
Show interest in understanding the principles of DC generator operation.

Psychomotor Domain:

Calculate generated EMF using given parameters.
Calculate terminal voltage using given parameters.

Work collaboratively with peers to solve problems related to DC generator voltage calculations.

Reference Materials

The following resources were used in planning this lesson:

Senior Secondary Schools Education Curriculum
State Unified Scheme of Work
D. N. Anyakoha, New School Physics for Senior Secondary Schools.
Practical Physics for Senior Secondary Schools.

Instructional Materials

The teacher will teach this lesson with the aid of:

Worked examples on a chart or projector.
Scientific calculators.
Whiteboard or blackboard and markers/chalk.
Diagrams of DC generator circuits.

Rationale for the Lesson

This lesson helps pupils understand how DC generators produce electricity and the factors that influence the voltage they generate. It enables them to apply mathematical formulas to practical electrical engineering problems, which is important for future studies and careers in technical fields.

Prerequisite/Previous Knowledge

Pupils have prior knowledge of basic electrical concepts, including voltage, current, resistance, and the principles of electromagnetic induction.

Lesson Content/Board Summary

DC GENERATOR VOLTAGE CALCULATIONS

1. Generated Electromotive Force (EMF)

The generated electromotive force (EMF) is the voltage induced in the armature conductors of a DC generator due to electromagnetic induction. It represents the total voltage produced by the generator before any internal voltage drops.

The formula for generated EMF (E) is:

E = (ΦZN/60A) * P

Where:

E = Generated EMF (Volts, V)
Φ (Phi) = Flux per pole (Webers, Wb)
Z = Total number of armature conductors
N = Speed of the armature (revolutions per minute, RPM)
P = Number of poles
A = Number of parallel paths in the armature winding (A = P for lap winding; A = 2 for wave winding)

Factors affecting generated EMF:

Flux per pole (Φ)
Number of armature conductors (Z)
Speed of the armature (N)
Number of poles (P)
Type of armature winding (which determines A)

Worked Example 1: Calculating Generated EMF

A 4-pole DC generator with a lap-wound armature has 500 conductors. The flux per pole is 0.02 Wb, and the armature rotates at 1200 RPM. Calculate the generated EMF.

Step 1: Identify given parameters.

P = 4 poles
Armature winding = Lap-wound, so A = P = 4
Z = 500 conductors
Φ = 0.02 Wb
N = 1200 RPM

Step 2: State the formula for generated EMF.

E = (ΦZN/60A) * P

Step 3: Substitute the values into the formula and calculate.

E = (0.02 Wb * 500 * 1200 RPM / (60 * 4)) * 4

E = (12000 / 240) * 4

E = 50 * 4

E = 200 V

Therefore, the generated EMF is 200 Volts.

2. Output Voltage (Terminal Voltage)

The output voltage, also known as the terminal voltage (V_t), is the voltage available at the terminals of the generator for connection to a load. It is less than the generated EMF due to voltage drops within the generator’s armature winding.

The formula for terminal voltage (V_t) in a DC generator is:

V_t = E – I_a R_a

Where:

V_t = Terminal voltage (Volts, V)
E = Generated EMF (Volts, V)
I_a = Armature current (Amperes, A)
R_a = Armature resistance (Ohms, Ω)

The term I_a R_a represents the voltage drop across the armature winding due to its internal resistance when current flows through it.

Worked Example 2: Calculating Terminal Voltage

A DC generator generates an EMF of 200 V. If the armature resistance is 0.5 Ω and the armature current is 10 A, calculate the terminal voltage.

Step 1: Identify given parameters.

E = 200 V
R_a = 0.5 Ω
I_a = 10 A

Step 2: State the formula for terminal voltage.

V_t = E – I_a R_a

Step 3: Substitute the values into the formula and calculate.

V_t = 200 V – (10 A * 0.5 Ω)

V_t = 200 V – 5 V

V_t = 195 V

Therefore, the terminal voltage is 195 Volts.

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 asks pupils to recall what a DC generator is and how it produces electricity. The teacher then introduces the topic of calculating the voltage generated by a DC generator.
Pupils’ Activity: Pupils respond to questions and listen attentively to the introduction of the new topic.
Learning Point: Pupils recall previous knowledge and are introduced to the lesson’s focus.

Step 2: Explanation of Generated EMF

Time: 7 minutes
Teaching Skill: Explanation/Lecture
Teacher’s Activity: The teacher explains the concept of generated EMF, its significance, and presents the formula E = (ΦZN/60A) * P, clearly defining each variable and its unit.
Pupils’ Activity: Pupils listen, take notes, and ask questions for clarification on the formula and variables.
Learning Point: Pupils understand the definition and formula for generated EMF.

Step 3: Calculation of Generated EMF

Time: 7 minutes
Teaching Skill: Demonstration/Problem Solving
Teacher’s Activity: The teacher solves Worked Example 1 on the board, demonstrating the step-by-step calculation of generated EMF, explaining each step clearly.
Pupils’ Activity: Pupils observe the steps, copy the example into their notebooks, and participate by suggesting values or steps.
Learning Point: Pupils learn how to apply the formula to calculate generated EMF.

Step 4: Explanation of Terminal Voltage

Time: 7 minutes
Teaching Skill: Explanation/Lecture
Teacher’s Activity: The teacher explains the concept of terminal voltage, distinguishing it from generated EMF, and presents the formula V_t = E – I_a R_a, defining each variable.
Pupils’ Activity: Pupils listen, take notes, and ask questions about the difference between generated and terminal voltage.
Learning Point: Pupils understand the definition and formula for terminal voltage.

Step 5: Calculation of Terminal Voltage

Time: 7 minutes
Teaching Skill: Demonstration/Problem Solving
Teacher’s Activity: The teacher solves Worked Example 2 on the board, demonstrating the step-by-step calculation of terminal voltage.
Pupils’ Activity: Pupils observe, copy the example, and participate by checking calculations.
Learning Point: Pupils learn how to apply the formula to calculate terminal voltage.

Step 6: Class Work/Practice

Time: 5 minutes
Teaching Skill: Application
Teacher’s Activity: The teacher gives a short problem for pupils to solve individually or in pairs, involving both generated EMF and terminal voltage calculations.
Pupils’ Activity: Pupils work on the given problem, applying the learned formulas.
Learning Point: Pupils practice applying the formulas independently.

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 generated electromotive force (EMF).
State the formula for calculating generated EMF, defining all symbols.
What is terminal voltage in a DC generator?
State the formula for terminal voltage.
A 6-pole DC generator with a wave-wound armature has 400 conductors. The flux per pole is 0.03 Wb, and it rotates at 1000 RPM. Calculate the generated EMF.

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, emphasizing the importance of understanding and correctly applying the formulas for DC generator voltage calculations. The teacher assigns homework.
Pupils’ Activity: Pupils listen to the summary and copy down the homework assignment.
Learning Point: Pupils reinforce their understanding and are given tasks for further practice.

Lesson Keywords

EMF – Electromotive Force, the voltage generated in a conductor.
Generated Voltage – The total voltage produced by a generator.
Terminal Voltage – The voltage available at the output terminals of a generator.
Armature – The rotating part of a DC machine containing conductors.
Flux per pole (Φ) – The magnetic field strength produced by each pole.
Armature resistance (R_a) – The internal resistance of the armature winding.
Armature current (I_a) – The current flowing through the armature winding.

Differentiation

For pupils who are struggling, the teacher will provide simplified examples and extra guidance on formula application. Advanced pupils will be given more complex problems involving rearranging formulas or additional parameters to calculate.

Note for teachers using this lesson plan

Ensure pupils understand the practical implications of voltage drops and the difference between generated and terminal voltage. Encourage them to draw simple circuit diagrams to visualize the components. Emphasize the correct use of units in all calculations.