Resistors, Capacitors and Inductors Are Not as They Appear
Paul Benjamin Crilly, Tooran Emami · 2020
Abstract Abstract –This paper presents an analysis of the basic elements of an electrical circuit in order that undergraduate engineering students will experience, and thereby understand the non-ideal nature of electrical components. It is motivated by the fact that many electrical engineering students, after they have completed their first circuits course believe that the assigned or measured values of a given resistor (R), inductor (L) or capacitor (C) are within the manufacturer’s stated tolerances and are in fact pure Rs, Ls and Cs. They also assume these components when connected to form a circuit will behave as a lumped parameter, time invariant system whose response can be predicted using a mathematical model based on measured or stated values. This paper demonstrates a practical experience that shows this is not always the case at frequencies above a few MHz. In a junior level laboratory, students discover that a coil will have a resonant frequency that is caused by parasitic or stray capacitance, that a resistor or capacitor lead whose length, l, is greater than 0.01 times the wavelength (i.e. l > 0.1λ )will have a significant inductive component that cannot be ignored, and that an iron core choke’s inductance is affected by its input signal’s frequency. The objective is to provide some practical, hands on experiences so that students can experience for themselves that resistors, inductors and capacitors are not at all what they seem and thereby develop deeper insight into the behavior of electrical components. The ultimate goal of this understanding is to make them more competent at design and analysis of electrical systems.