Capacitors and calculus

Chapter 13.2 Capacitors and calculus

Lessons In Electric Circuits Volume I – DC Book
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Summary of Contents

Lessons In Electric Circuits Volume I – DC Book

  • 444CHAPTER 13. CAPACITORS• When a capacitor is faced with an increasing voltage, it acts as a load: drawing currentas it absorbs energy (current going in the negative side and out the positive side, like aresistor).• When a capacitor is faced with a decreasing voltage, it acts as a source: supplying currentas it releases stored energy (current going out the negative side and in the positive side,like a battery).• The ability of a capacitor to store energy in the form of an electric field (and consequentlyto oppose changes in voltage) is called capacitance. It is measured in the unit of the Farad(F).• Capacitors used to be commonly known by another term: condenser(alternatively spelled”condensor”).13.2Capacitors and calculusCapacitors do not have a stable ”resistance” as conductors do. However, there is a definitemathematical relationship between voltage and current for a capacitor, as follows:i =dvdtWhere,CC = Capacitance in Faradsdvdt= Instantaneous rate of voltage change(volts per second)"Ohm’s Law" for a capacitori = Instantaneous current through the capacitorThe lower-case letter ”i” symbolizes instantaneouscurrent, which means the amount ofcurrent at a specific point in time. This stands in contrast to constant current or averagecurrent (capital letter ”I”) over an unspecified period of time. The expression ”dv/dt” is oneborrowed from calculus, meaning the instantaneous rate of voltage change over time, or therate of change of voltage (volts per second increase or decrease) at a specific point in time,the same specific point in time that the instantaneous current is referenced at. For whateverreason, the letter vis usually used to represent instantaneous voltage rather than the lettere. However, it would not be incorrect to express the instantaneous voltage rate-of-change as”de/dt” instead.In this equation we see something novel to our experience thusfar with electric circuits: thevariable of time. When relating the quantities of voltage, current, and resistance to a resistor,it doesn’t matter if we’re dealing with measurements taken over an unspecified period of time(E=IR; V=IR), or at a specific moment in time (e=ir; v=ir). The same basic formula holds true,because time is irrelevant to voltage, current, and resistance in a component like a resistor.