Context

Physics permeates all areas of our lives, and in our daily life, we come across concepts that are explained by it. One of these concepts is electrical resistance and, in particular, resistors in parallel. Resistors are components and devices that function to offer opposition to the flow of electric current, a concept we call electrical resistance.

The parallel circuit is one of the most common circuits in our lives. It allows electricity to continue flowing even if one of the components fails. This is due to the nature of the parallel circuit: in a parallel circuit, electric current has the possibility to follow more than one path. Therefore, when one component fails, the electric current has other paths to follow, thus allowing the other components to continue functioning.

Understanding the concepts associated with resistors in parallel is crucial for understanding many things around us. From simple devices like a cell phone charger to complex circuits in large industrial equipment, physics is in everything we do.

Introduction

It is essential that we understand the behavior of resistors in parallel in an electrical circuit. To begin, we must first understand what it means for a resistor to be in parallel. In a parallel circuit, the entry points (i.e., the beginning of the resistor) are connected to the same point, and the exit points (i.e., the end of the resistor) are connected to the same point. This means that the same voltage applies to all resistors in a parallel circuit.

The next step is to understand how current behaves in a parallel resistor circuit. Electric current in a parallel circuit is divided among the resistors. The amount of current each resistor receives is inversely proportional to its resistance. Therefore, a resistor with higher resistance will receive less current, and a resistor with lower resistance will receive more current.

Finally, we will learn how to calculate the total resistance in a parallel resistor circuit. Unlike series circuits, where we simply add the resistances, in a parallel circuit, the inverse of the total resistance is the sum of the inverses of the individual resistances. This formula is only valid for parallel circuits and is one of several ways that parallel circuits differ from series circuits.

Practical Activity

Activity Title: Building and Analyzing a Parallel Resistor Circuit

Project Objective:

This project aims to have students build a parallel resistor circuit, perform measurements and analysis on the circuit's operation, and compare experimental results with theoretical predictions. This will be done through the integration of Physics and Mathematics learning, emphasizing interdisciplinarity and teamwork.

Detailed Project Description:

The project will be carried out by groups of 3 to 5 students and must be completed within a 2-week period, allowing for over twelve hours of work per student.

The groups will be tasked with creating and testing an electrical circuit with resistors in parallel. They will pre-calculate the current and voltage across each resistor and the power supply, and then confirm their predictions with experimental measurements. Students will have to identify the effects of different resistors on the total current and voltage in their circuits and analyze the role of resistance in the sharing of electrical energy.

It is important for students to fully understand the reason for each step of the experiment. Therefore, they should consult reliable sources of information, participate in group discussions, and even seek external help if necessary.

Required Materials:

• Resistors (various values)
• Multimeter
• Wires
• Battery or power supply
• Connectors

Step-by-Step Guide for Activity Execution:

1. Each group must design an electrical circuit including at least three resistors in parallel.
2. Calculate the total resistance of the circuit and the current through each resistor using the appropriate equations.
3. Physically build the designed circuit.
4. Using the multimeter, measure the voltage across each resistor and the current passing through each of them. Record the data.
5. Compare the experimental data with the previously calculated theoretical results.
6. Evaluate the impact of changing the resistance in one of the resistors. Perform calculations and measurements after the change.
7. Record all observations, calculations, and measurements in a lab notebook.
8. Discuss the findings with the group and draw conclusions.

Project Deliverables:

1. Report: Each group must produce a report documenting the work done, the discoveries made, the sources consulted, and the conclusions drawn.

   • Introduction: Provide context for the topic, its relevance and real-world application, as well as the objective of this project.
   • Development: Explain the theory behind resistors in parallel, detail the activity, indicate the methodology used, and finally present and discuss the results obtained.
   • Conclusions: Summarize the main points of the report, highlight the learnings obtained, and draw conclusions about the project.
   • Bibliography: Indicate the sources relied upon to work on the project such as books, web pages, videos, etc.

2. Presentation: In addition to the report, students will be invited to present their results to the classroom, where they should explain what they did, show their circuit in operation, and discuss their results and conclusions.