Applications of Systems of Equations: An Electronic Circuit
Does the real-world application of science depend on mathematics? In this activity, students answer this question as they experience a real-world application of systems of equations. Given a system of linear equations that mathematically models a specific circuit—students start by solving a system of three equations for the currents. After becoming familiar with the parts of a breadboard, groups use a breadboard, resistors and jumper wires to each build the same (physical) electric circuit from the provided circuit diagram. Then they use voltmeters to measure the current flow across each resistor and calculate the current using Ohm’s law. They compare the mathematically derived current values to the measured values, and calculate the percentage difference of their results. This leads students to conclude that real-world applications of science do indeed depend on mathematics! Students make posters to communicate their results and conclusions. A pre/post-activity quiz and student worksheet are provided. Adjustable for math- or science-focused classrooms.
An electronic circuit.Copyright 2001 Nicola Asuni, Wikimedia Commons CC BY-SA 3.0 https://commons.wikimedia.org/wiki/File:Electronic_circuit.jpg
Are all circuits the same? When you flip a switch that controls a circuit, is it only turning it on and off? The answer to this question depends on what the circuit is designed to do. The power portion of the electric circuit simply powers machines with electric current flow, whereas an electronic circuit can interpret signals, give commands and/or perform tasks. Engineers use both circuit types in most of the sophisticated devices we depend on daily such as cell phones, computers, lamps, washers and dryers, cars and many more. This activity shows students how the myriad electronic circuits so essential in our lives can be understood as and defined as systems of equations.
After this activity, students should be able to:
- Apply the concepts of systems of equations to real-world situations.
- Explain the importance of systems of equations in engineering.
- Construct a circuit using a breadboard, resistors, voltage source and wires.
- Use a voltmeter to measure voltages in a circuit.
- Compare measured and calculated values by calculating the percentage difference.
- Explain how they are impacted by this real-world experience and its connection with mathematics.