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Experiment 7 - The Resistor Capacitor Circuit Learning Objectives: Understand the short and long time behavior of circuits containing capacitors. Understand the and the mathematical relationshin between the current through the circuit as a function time, resistance, capacitance, and potential difference 1. Understanding the models for the behavior of a capacitor in a circuit A capacitor is a device that stores energy in a circuit as potential energy in an electric field. In the simple circuit drawn on the night, the circuit diagram element for a capacitor also illustrates a basic model of a capacitor as a set of parallel plates of conductive material with a gap between them. Initially, when the circuit is open (as shown) there is no net electric charge on the plates. Once the switch is closed then the circuit is complete the electric charges move through the circuit. The electric field in the circuit drives electrons from capacitor plate h to the positive Figure 1. A capacitor in a circuit. terminal of the battery. As it loses electrons plate h gains a net positive charge. Simultaneously, the electric field drives just as many electrons from the negative terminal of the battery onto platel, which creates a net negative charge on plate. The letters h and I are used here as the plate that gains a net positive charge is said to be at a hlah potential and the plate the gains a net negative charge is said to be at a low potential. 1. With the switch open, what is the potential difference between the plates which are separated by a distance d? 2. What is the magnitude of the electric field between the capacitor plates at this time? Recall that the strength of the electric field can be expressed as a potential difference divided by a distance. 3. Consider the circuit divided in half. One half is between the positive terminal of the battery and plate h and the other half is between the negative terminal of the battery and plate L. When the switch is closed, current flows through the circuit and charges build up on the capacitor; eventually the potential difference between the plates will be the same as the potential difference of the battery. At that time, the potential on plate h is the same as the potential of the positive terminal of the battery (similarly for the plate I and the negative terminal). A capacitor in this state is said to be "fully charged." a. When the capacitor is "fully charged", describe the electric field in the "half" or part of the circuit between the positive terminal of the battery and plate h. What about between the negative terminal of the battery and plate 1? Based on your responses, what can you say about the magnitude of current flowing through the circuit? The charge Q on each plate and the potential difference V between the plates are directly proportional to each other and can be expressed as Q = CV. The constant of proportionality, Cin the equation, is called the capacitance of the capacitor. Note that capacitance is the ability of an object to store an electrical charge; any object that can be electrically charged exhibits capacitance. Because capacitors are able to nergy they act like small batteries and can store or release the energy as required. The capacitance depends only on the geometry of the plates and not on the charge or potential difference between the plates. The unit of capacitance is the farad (denoted as F), which is defined as 1 F = 1 C/V or 1 coulomb/volt. Page 4

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Questions about a circuit in which a capacitor is connected to a battery via a switch .The switch is initially open.
- each 1. With the switch open the potential difference a between the plater is zero. (Answer) We know, v z G . When the switch is open net charge of ong capacitor plate, gzo. Then vzo as c is non zero .. 2. Ezy where is the electric field il between the capacitor plater o separated by distance d.o. When the switch is open, Vzo and hence Ezo. electric field between the capacitor plates is o when the switch is open. (Answer) . . 3. When the capacitor is fully charged, the • Rotential difference v between the positive terminal of the battery and the plate h is o. As Ear inside any conducting path potential difference at whose two ends isv, the electric field dectween the positive terminal of the battery and the plate h of the capacitor is o when the capacitor is fully charged .(Answer)! potential difference dictween Similarly a the negative terminal of the battery and the plate e of the fully charged capacitor being 0, the electric field dectween the negative terminal at and the plate & is also o : (Answer )

free As electric field in the conducting paths in the capacitor-battery circuit is o , when the capacitor is fully charged , the fecharger in the conducting paths have no net movement, so the magnitude of current flowing in the circuit is o when the capacitor is fully charged (Answer ) è Rc).... . V(t) a Valo- At the instant the battery is connected (to ) (1) gives the voltage across the capacitor z V(o) z V watt (1-1) 2 V leatt (1-1) 2 Vesatt. 20. (Answer)