Physics
Chapter 19: 5-8
Web Lecture
RC Circuits
Introduction
Leitet man einen constanten galvanischen Strom durch eine Metallscheibe, so wird sich die Elektricität in dieser auf eine bestimmte Weise vertheilen. Die Art der Vertheilung kann man nach den von Ohm aufgestellten Principien theoretisch ermitteln. Ich habe die dazu nöthige der Scheibe ein stationhrer geworden sey, in dem Falle durchgeführt, dass die Scheibe eine kreisförmige ist, und dass die Elektricität durch einen Draht in sie hinein, durch einen zweiten aus ihr heraustrete. Das Resultat wurde insbesonders einfach, wenn der Ein- und der Austrittspunkt in der Peripherie der Scheibe liegen; in diesem Falle habe is dasselbe durch Versuche geprüft und, wie es mir scheint, eine hinreichende Bestätigung gefunden. Ich vill heir zuerst die theoretischen Betrachtungen angeben, und dann die Experimente beschreiben, die ich angestellt habe.
Suppose we direct a constant galvanic current through a metal plate; the electricity in this plate will distribute itself in a determinate fashion. We can determine the distribution theoretically following the principles established by Ohm. I have made the necessary calculation, under the conditions that the state of the plate is constant, that the plate is circular, and that the electricity enters the plate through one wire and exists through a second wire. The result would be simple if the entrance and exit points lay on the periphery of the plate; for this case I have tested the calculation through experiment and, it appears to me, I have found a sufficient confirmation. I will first give the theoretical considerations, thenI will describe the experiment.
— Gustav Kirchhoff, Über den Durchgang eines elektrischen Stromes durch eine Ebene, insbesondere durch eine kreisförmige
Outline
Current, Resistors, and Kirchhoff's Laws Part II
We now try to analyze circuits by applying some basic rules, called Kirchhoff's rules. These rules emphasize the physical reality that current is a stream of electrons, taking paths controlled by the amount of other electron traffic.
DC Circuits and Capacitance
Since Q = CV the result of putting capacitors in series is the opposite of putting resistors in series: the net or equivalent capacitance of series capacitors is 1/Ceq = 1/C1 + 1/C2 + 1/C3. The equivalent capacitance is smaller than the the smallest capacitor component. This resembles the result of putting resistors in parallel.
Likewise, the result of putting capacitors in parallel resembles the result of putting resistors in series: Ceq = C1 + C2 + C3.
The diagram below shows the analysis of a complex capacitance circuit with a parallel loop and a series loop. The total charge storage capacity of the circuit is 240 μC.
Resistor and Capacitance Circuits
Capacitors and resistors can be combined to create circuits that store charge on a capacitor, then use the charge to power a load for a discrete period of time. These are especially useful where the switch is some device that creates a connection in response to charge limit or potential, such as a vacuum bulb.
Practice with the Concepts
Discussion Points
- In an RC Circuit, current flows from the battery until the capictor is completely charged. Is the total energy supplied by the battery equal to the total energy stored by the capacitor? If not, where does the extra energy go?
- What would happen if you mistakenly used an ammeter where you needed to use a voltmeter?
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