Inductors and calculus

Chapter 15.2 Inductors and calculus

Lessons In Electric Circuits Volume I – DC Book
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Lessons In Electric Circuits Volume I – DC Book

  • 15.2. INDUCTORS AND CALCULUS485• Inductors react against changes in current by dropping voltage in the polarity necessaryto oppose the change.• When an inductor is faced with an increasing current, it acts as a load: dropping voltageas it absorbs energy (negative on the current entry side and positive on the current exitside, like a resistor).• When an inductor is faced with a decreasing current, it acts as a source: creating voltageas it releases stored energy (positive on the current entry side and negative on the currentexit side, like a battery).• The ability of an inductor to store energy in the form of a magnetic field (and consequentlyto oppose changes in current) is called inductance. It is measured in the unit of the Henry(H).• Inductors used to be commonly known by another term: choke. In large power applica-tions, they are sometimes referred to as reactors.15.2Inductors and calculusInductors do not have a stable ”resistance” as conductors do. However, there is a definitemathematical relationship between voltage and current for an inductor, as follows:dtWhere,dt"Ohm’s Law" for an inductorv =diLv = Instantaneous voltage across the inductorL = Inductance in Henrysdi= Instantaneous rate of current change(amps per second)You should recognize the form of this equation from the capacitor chapter. It relates onevariable (in this case, inductor voltage drop) to a rate of changeof another variable (in thiscase, inductor current). Both voltage (v) and rate of current change (di/dt) are instantaneous:that is, in relation to a specific point in time, thus the lower-case letters ”v” and ”i”. As withthe capacitor formula, it is convention to express instantaneous voltage as vrather than e, butusing the latter designation would not be wrong. Current rate-of-change (di/dt) is expressed inunits of amps per second, a positive number representing an increase and a negative numberrepresenting a decrease.Like a capacitor, an inductor’s behavior is rooted in the variable of time. Aside from anyresistance intrinsic to an inductor’s wire coil (which we will assume is zero for the sake of