Lesson plan

Topicmf4840050e6284530_1528449000663_0Topic

Electric receivers connected in parallel

Levelmf4840050e6284530_1528449084556_0Level

Second

Core curriculummf4840050e6284530_1528449076687_0Core curriculum

VI. Electricity. The student:

13) draws diagrams of electric circuits consisting of one energy source, one electrical receiver, meters and switches; uses graphical symbols of these elements.

Timingmf4840050e6284530_1528449068082_0Timing

45 minutes

General learning objectivesmf4840050e6284530_1528449523725_0General learning objectives

Derivation of the formula for equivalent resistance in a parallel connection.

Key competencesmf4840050e6284530_1528449552113_0Key competences

1. Defining equivalent resistanceequivalent resistanceequivalent resistance.

2. Experimental test of voltages on resistors connected in parallel.

3. Experimental verification of the formula for equivalent resistance in a parallel connectionparallel connectionparallel connection.

Operational (detailed) goalsmf4840050e6284530_1528450430307_0Operational (detailed) goals

The student:

- defines the concept of equivalent resistance,

- knows and applies the formula for equivalent resistance in a parallel connection.

Methodsmf4840050e6284530_1528449534267_0Methods

1. Discussion developing in the course of common problem solving by a class or group.

2. Organizing and applying the results obtained in new tasks of a practical or theoretical nature.

Forms of workmf4840050e6284530_1528449514617_0Forms of work

1. Work in groups during the experiment.

2. Work in groups on the formulation and verification of the research hypothesis.

Lesson stages

Introductionmf4840050e6284530_1528450127855_0Introduction

Prepare answers to introductory questions for the lesson.

1. What is electric current?

2. Introduce Ohm's law.

3. Define the resistance of the conductor.

4. How/will the resistance of the conductor change when we increase the voltage applied to it?

Proceduremf4840050e6284530_1528446435040_0Procedure

When resistors are connected in parallel?

[Illustration 1]

The parallel connectionparallel connectionparallel connection forces the same voltage on each of the resistors. Both ends of each resistor are connected to exactly the same points of the circuit.

Experiment 1

Research hypothesis:

In the parallel connection of resistors, the sum of the currents flowing through each resistor is equal to the current flowing from the source.

1. You will need several different resistors, an ammeter, a voltmeter and a voltage source to perform the experiment.

2. Build the system according to the diagram below.

[Illustration 2]

3. By changing the position of the ammeter, determine the currents flowing through the individual resistors and the current flowing from the voltage source.

4. Measurements results should be entered into the measurement table.

[Table 1]

5. In order to eliminate errors during the experiment, perform several measurements.

6. After completing the experiment, draw the appropriate conclusions.

Conclusion:

In a parallel connection, the sum of the currents flowing through each resistor is equal to the total current flowing out of the source (within the limits of measurement errors):

I_{1} + I_{2} + I_{3} + I_{4} + I_{5} = I_{total}

Definition of equivalent resistanceequivalent resistanceequivalent resistance.

The equivalent resistance of the resistors circuit is equal to the resistance of such a resistor which used instead of the resistor circuit will not change the current flowing from the voltage source.mf4840050e6284530_1527752263647_0The equivalent resistance of the resistors circuit is equal to the resistance of such a resistor which used instead of the resistor circuit will not change the current flowing from the voltage source.

Derivation of the formula for equivalent resistance in a parallel connectionparallel connectionparallel connection.

Consider a circuit of resistors connected in parallel.

[Illustration 3]

Let the currents flowing through individual resistors be equal to: $I_{1}, I_{2}, I_{3}, I_{4}, I_{5}$ . The resistors circuit is supplied with voltage U. Under Ohm's law, we have:

I_{1} = \frac{U}{R_{1}}

I_{2} = \frac{U}{R_{2}}

I_{3} = \frac{U}{R_{3}}

I_{4} = \frac{U}{R_{4}}

I_{5} = \frac{U}{R_{5}}

If we use substitute equivalent resistanceequivalent resistanceequivalent resistance instead of all resistors, then:

I_{total} = \frac{U}{R_{equiv}}

Substituting above relations into the formula:

I_{1} + I_{2} + I_{3} + I_{4} + I_{5} = I_{total}

after simplification it leads to the final result:

\frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + \frac{1}{R_{4}} + \frac{1}{R_{5}} = \frac{1}{R_{equiv}}

Final conclusion:

In a parallel connection, the inverse of the equivalent resistance is the sum of the inverse of resistances of individual resistors.mf4840050e6284530_1527752256679_0In a parallel connection, the inverse of the equivalent resistance is the sum of the inverse of resistances of individual resistors.

Experiment 2

Research hypothesis:

In the parallel connectionparallel connectionparallel connection, the inverse of the equivalent resistanceequivalent resistanceequivalent resistance is the sum of the inverse of the resistances of individual resistors.

1. You will need several different resistors, an ammeter, a voltmeter and a voltage source to perform the experiment.

2. Build the system according to the diagram below.

[Illustration 4]

3. In the way known to you, determine the resistances of individual resistors.

4. Calculate the total resistance of the resistor system.

5. Enter the results into the measurement table.

[Table 2]

6. In order to eliminate errors during the experiment, perform several measurements, preferably each time rearranging the order of the resistors.

7. After completing the experiment, draw the appropriate conclusions.

Conclusion:

If the experiment was performed correctly, then within the limits of measurement errors:

\frac{1}{R_{1}} + \frac{1}{R_{2}} + \frac{1}{R_{3}} + \frac{1}{R_{4}} + \frac{1}{R_{5}} = \frac{1}{R_{equiv}} = \frac{1}{R_{total}}

It is, therefore, a confirmation of the formula derived theoretically.

[Slideshow]

Lesson summarymf4840050e6284530_1528450119332_0Lesson summary

- Kirchhoff's first law: the sum of the currents flowing into the node and the sum of the currents flowing out of it are equal.

- The voltage applied to the resistors connected in parallel and the voltage on the individual resistors have the same value.

- To calculate the inverse of the total resistance of resistors connected in parallel, the inverse of resistances of individual resistors should be added.

Selected words and expressions used in the lesson plan

equivalent resistanceequivalent resistanceequivalent resistance

parallel connectionparallel connectionparallel connection

principle of charge conservationprinciple of charge conservationprinciple of charge conservation

voltage dividervoltage dividervoltage divider

voltage dropvoltage dropvoltage drop

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mf4840050e6284530_1528449552113_0

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mf4840050e6284530_1528449534267_0

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equivalent resistance1

parallel connection1

principle of charge conservation1

voltage divider1

voltage drop1

Scenariusz

Topicmf4840050e6284530_1528449000663_0Topic

Lesson stages

Selected words and expressions used in the lesson plan