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Modeling Scenario

4-060-CircuitTuner-ModelingScenario

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

Keywords: resistance ciircuit tuned mass tuner frequency Kirchhoff voltage gain frequency response amplitude s Voltage Law inductance capacitor I am currently working in redesining an existing microbiology course. I would like to be part of ed

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Abstract

Resource Image We present essential definitions and laws for the study of simple RLC electrical circuits and build a differential equation model using these notions. We describe how such a circuit can be used to tune a radio to a certain input frequency.

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Article Context

Resource Type
Differential Equation Type
Qualitative Analysis
Technology
Approach
Key Scientific Process Skills
Pedagogical Approaches
Bloom's Cognitive Level

Description

Differential equations prove exceptional at modeling electrical circuits. In fact the very simple circuit, which is fundamental to larger circuit building, and three of the most fundamental electrical objects, a resistor, a capacitor, and inductor, can be modeled by a constant coefficient, linear, second order differential equation. We consider a RLC circuit show in the Modeling Scenario.

The EMF E(t) represents an Electromotive Force generated by an excess of electrons on one side of a barrier (the Switch) and a paucity of electrons on the other side of the barrier. When the switch is thrown the electrons in the excess area (say to the left of the circle marked EMF) seek to take the path of least resistance to get to the location of the paucity of electrons (to the right of the circle marked EMF).

Thus we say there is a potential awaiting the switch to be thrown and that potential (just like water held high and then released to run down a descending track) causes electrons to flow clockwise through the capacitance (C), through the resistance (R), and finally through the inductance (L) until these electrons are ``home" to the region of paucity of electrons.

Article Files

Authors

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

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