Lesson Note on Electric Field: Galvanometer Conversions and Wheatstone Bridge for SSS 2

Class: Senior Secondary School 2 (SS2 / SSS2)
Term: Second Term
Week: 10
Age: 16 years
Duration: 45 minutes
Subject: Physics
Curriculum Theme: Electrical Measurements
Previous Lesson: Electric Fields: E.M.F, Internal Resistance and Potentiometer Use.
Topic: ELECTRIC FIELD
Subject Matter: Shunts and multipliers (galvanometer conversions), principle of the potentiometer (null method), Wheatstone bridge (resistance comparison), meter bridge (practical Wheatstone bridge)

Specific Objectives

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

Cognitive Domain:

• Define shunt and multiplier.
• State the principle of a potentiometer.
• Explain the working of a Wheatstone bridge.
• Describe the construction and working of a meter bridge.

Affective Domain:

• Appreciate the importance of accurate electrical measurements.
• Develop an interest in practical circuit applications.

Psychomotor Domain:

• Calculate shunt and multiplier resistances for galvanometer conversion.
• Sketch a simple potentiometer circuit.
• Set up a Wheatstone bridge circuit for resistance comparison.
• Determine an unknown resistance using a meter bridge.

Social Domain:

• Collaborate with peers during practical activities.

Reference Materials

The following resources were used in planning this lesson:

• Senior Secondary Schools Education Curriculum
• State Unified Scheme of Work
• New School Physics by M.W. Anyakoha

Instructional Materials

The teacher will teach this lesson with the aid of:

• Galvanometer
• Resistors (known and unknown)
• Connecting wires
• Battery/Power supply
• Potentiometer wire
• Meter bridge apparatus
• Jockey
• Ammeter
• Voltmeter

Rationale for the Lesson

This lesson helps pupils understand how galvanometers can be converted into useful ammeters and voltmeters. It also introduces methods for accurately measuring resistance and potential differences in circuits, which are important skills for further studies in physics and engineering.

Prerequisite/Previous Knowledge

Pupils are expected to have prior knowledge of basic concepts of current electricity, resistance, Ohm’s law, and the working of a galvanometer.

Lesson Content/Board Summary

Electrical Measuring Devices

1. Shunts (Galvanometer to Ammeter)

A shunt is a low resistance connected in parallel with a galvanometer to convert it into an ammeter. An ammeter is used to measure large currents and has a very low internal resistance.

Formula for Shunt Resistance (R_s):

R_s = (I_g * G) / (I – I_g)

• I_g = Full scale deflection current of the galvanometer
• G = Resistance of the galvanometer
• I = Total current to be measured (range of the ammeter)

Worked Example 1: Shunt Calculation

A galvanometer with a resistance of 50 Ω gives a full-scale deflection with a current of 10 mA. Calculate the resistance of the shunt required to convert it into an ammeter of range 5 A.

Step 1: Identify given values.
G = 50 Ω
I_g = 10 mA = 0.01 A
I = 5 A

Step 2: Apply the shunt formula.
R_s = (I_g * G) / (I – I_g)

Step 3: Substitute and calculate.
R_s = (0.01 * 50) / (5 – 0.01)
R_s = 0.5 / 4.99
R_s ≈ 0.1002 Ω
Note: The shunt resistance is very small and connected in parallel.

2. Multipliers (Galvanometer to Voltmeter)

A multiplier is a high resistance connected in series with a galvanometer to convert it into a voltmeter. A voltmeter is used to measure potential differences and has a very high internal resistance.

Formula for Multiplier Resistance (R_m):

R_m = (V / I_g) – G

• V = Total voltage to be measured (range of the voltmeter)
• I_g = Full scale deflection current of the galvanometer
• G = Resistance of the galvanometer

Worked Example 2: Multiplier Calculation

A galvanometer with a resistance of 50 Ω gives a full-scale deflection with a current of 10 mA. Calculate the resistance of the multiplier required to convert it into a voltmeter of range 50 V.

Step 1: Identify given values.
G = 50 Ω
I_g = 10 mA = 0.01 A
V = 50 V

Step 2: Apply the multiplier formula.
R_m = (V / I_g) – G

Step 3: Substitute and calculate.
R_m = (50 / 0.01) – 50
R_m = 5000 – 50
R_m = 4950 Ω
Note: The multiplier resistance is large and connected in series.

3. Potentiometer

A potentiometer is an instrument used for measuring or comparing electromotive forces (e.m.f.) and potential differences accurately. It works on the principle of the null method, where no current flows through the galvanometer when balanced.

Principle: The potential drop across any length of a wire of uniform cross-section and uniform composition is directly proportional to its length, provided a constant current flows through it.

Uses:

• Comparison of e.m.f.s of two cells.
• Measurement of internal resistance of a cell.
• Measurement of very small potential differences.

Pupils should be able to sketch a basic potentiometer circuit showing the driving cell, the test cell, galvanometer, and jockey.

4. Wheatstone Bridge

The Wheatstone bridge is an electrical circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component.

Principle (Balanced Condition): When the bridge is balanced (no current flows through the galvanometer), the ratio of resistances in the first pair of arms is equal to the ratio of resistances in the second pair of arms.

Formula:

P / Q = R / S

• P, Q, R are known resistances
• S is the unknown resistance

Pupils should be able to sketch a Wheatstone bridge circuit with four resistors and a galvanometer.

5. Meter Bridge (Slide Wire Bridge)

The meter bridge is a practical application of the Wheatstone bridge principle used to determine an unknown resistance or compare two resistances. It consists of a one-meter long wire of uniform cross-section stretched along a meter scale.

Construction: It has two gaps for connecting resistors, a galvanometer, a jockey, and a 1-meter long uniform resistance wire.

Formula for Unknown Resistance (S):

R / S = l₁ / l₂

Therefore, S = R * (l₂ / l₁)

• R = Known resistance in the left gap
• S = Unknown resistance in the right gap
• l₁ = Balancing length from the left end (where R is connected)
• l₂ = (100 – l₁) = Balancing length from the right end

Pupils should be able to sketch a meter bridge circuit showing the components and balancing lengths.

Worked Example 3: Meter Bridge Calculation

In a meter bridge experiment, the null point is found at 40 cm from the left end when a known resistance of 10 Ω is placed in the left gap. Determine the unknown resistance in the right gap.

Step 1: Identify given values.
R = 10 Ω
l₁ = 40 cm
l₂ = 100 – l₁ = 100 – 40 = 60 cm

Step 2: Apply the meter bridge formula.
S = R * (l₂ / l₁)

Step 3: Substitute and calculate.
S = 10 * (60 / 40)
S = 10 * 1.5
S = 15 Ω
Note: The unknown resistance is directly proportional to the balancing length on its side.

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 questions about their previous knowledge of galvanometers and basic circuit components.
Pupils’ Activity: Pupils respond to the questions, recalling concepts of current, resistance, and how a galvanometer detects current.
Learning Point: Pupils recall prior knowledge of basic electricity and galvanometers.

Step 2: Shunts and Multipliers

Time: 10 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher explains the concept of shunts and multipliers, their purpose, and derives the formulas for their resistances. The teacher solves worked examples on the board.
Pupils’ Activity: Pupils listen attentively, take notes, and ask questions for clarification. They observe the worked examples.
Learning Point: Pupils understand how to convert a galvanometer into an ammeter or voltmeter and can calculate the required resistances.

Step 3: Potentiometer

Time: 10 minutes
Teaching Skill: Explanation/Illustration
Teacher’s Activity: The teacher explains the principle of the potentiometer (null method) and its uses, drawing a simple circuit diagram on the board.
Pupils’ Activity: Pupils listen, observe the diagram, and copy notes. They identify the components and understand the null method.
Learning Point: Pupils grasp the principle and applications of a potentiometer.

Step 4: Wheatstone Bridge

Time: 5 minutes
Teaching Skill: Explanation/Illustration
Teacher’s Activity: The teacher explains the principle of the Wheatstone bridge, its balanced condition, and the relevant formula, drawing the circuit diagram.
Pupils’ Activity: Pupils pay attention, copy the diagram and formula, and understand the concept of balanced resistance ratios.
Learning Point: Pupils understand the working principle and formula of a Wheatstone bridge.

Step 5: Meter Bridge

Time: 5 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher explains the meter bridge as a practical Wheatstone bridge, describing its construction and principle. The teacher solves a worked example on the board.
Pupils’ Activity: Pupils observe the teacher’s explanation and the worked example, taking notes on the construction and formula.
Learning Point: Pupils understand the meter bridge and its use in determining unknown resistance.

Step 6: Practical Demonstration

Time: 5 minutes
Teaching Skill: Demonstration/Practical Activity
Teacher’s Activity: The teacher demonstrates the setup of a simple meter bridge or potentiometer circuit, highlighting key connections and the balancing procedure.
Pupils’ Activity: Pupils observe the demonstration carefully, asking questions about the practical aspects of setting up the circuit.
Learning Point: Pupils gain practical insight into setting up and using circuit measurement devices.

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 shunt and multiplier.
2. State the formula for calculating shunt resistance and explain the terms.
3. Describe the principle of a potentiometer.
4. Explain how a meter bridge is used to determine an unknown resistance.

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

Step 8: Conclusion

Time: 0 minutes
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarizes the key points of the lesson, emphasizing the importance of accurate electrical measurements and the role of these devices. The teacher assigns homework, which includes solving problems related to shunts, multipliers, and meter bridge calculations.
Pupils’ Activity: Pupils listen to the summary and copy down the assigned homework.
Learning Point: Pupils consolidate their understanding and apply learned concepts through homework.

Lesson Keywords

• Shunt – A low resistance connected in parallel with a galvanometer to increase its current range.
• Multiplier – A high resistance connected in series with a galvanometer to increase its voltage range.
• Potentiometer – A device used to measure or compare electromotive forces accurately using a null method.
• Wheatstone Bridge – An electrical circuit used to measure an unknown resistance by balancing two legs of a bridge.
• Meter Bridge – A practical form of the Wheatstone bridge used to determine unknown resistance.
• Null Method – A measurement technique where a galvanometer shows zero deflection, indicating no current flow.

Differentiation

For pupils who grasp concepts quickly, the teacher can provide additional challenging problems involving combined circuits or ask them to research advanced applications of these devices. For pupils needing more support, the teacher will provide simplified diagrams, repeat explanations, and offer one-on-one guidance during practical demonstrations.

Note for teachers using this lesson plan

Teachers should ensure that all practical demonstrations are conducted safely and that pupils understand the correct handling of electrical components. Emphasize the theoretical principles alongside the practical applications. Encourage pupils to draw and label circuit diagrams accurately in their notes.