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An overview of a lab experiment aimed at exploring the relationship between plate separation and voltage in a parallel plate capacitor. It discusses the formula for capacitance, the role of capacitors in storing energy, and the process of measuring capacitance and voltage. The document also includes instructions for setting up the experiment and collecting data.
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A capacitor is used to store electric charge. The more voltage (electrical pressure) you apply to the capacitor, the more charge is forced into the capacitor. Also, the more capacitance the capacitor possesses, the more a given voltage will force in more charge. This relation is described by the formula q=CV, where q is the charge stored, C is the capacitance, and V is the voltage applied. Looking at this formula, one might ask what would happen if charge were kept constant and the capacitance were varied. The answer is, of course, that the voltage will change! That is what you will do in this lab. The Lab Capacitor A parallel plate capacitor is a device used to study capacitors. It reduces to barest form the function of a capacitor. Real-world capacitors are usually wrapped up in spirals in small packages, so the parallel-plate capacitor makes it much easier to relate the function to the device. This capacitor works by building up opposite charges on parallel plates when a voltage is applied from one plate to the other. The amount of charge that moves into the plates depends upon the capacitance and the applied voltage according to the formula Q=CV, where Q is the charge in Coulombs, C is the capacitance in Farads, and V is the potential difference between the plates in volts. Capacitors store energy If a voltage is applied to a capacitor and then disconnected, the charge that is stored in the capacitor remains until the capacitor is discharged in some way. An electric field then exists between the plates, which allow the capacitor to store energy. This is one of the useful aspects of capacitors, the ability to store energy in an electric field so that can be utilized later on. What determines the capacitance? The surface area of the plates and the spacing between them determines the amount of charge that may be stored per volt applied. The larger the plates and the more closely they are spaced, the
Voltage Source Capacitor with charges
more charge can be stored for every volt of potential difference between the plates. The charge stored per volt applied is the capacitance, measured in Farads. Can altering the capacitance of a charged capacitor change its voltage? The lab capacitor is adjustable, so we can do an interesting experiment involving capacitance and voltage. If the capacitor has a constant charge, changing the capacitance should cause the voltage
How can capacitance of our capacitor be mathematically determined? For a parallel plate capacitor, the capacitance is given by the following formula: C = ε 0 A/d Where C is the capacitance in Farads, ε 0 is the constant for the permittivity of free space (8.85x10-^12 ), A is the area of the plates in square meters, and d is the spacing of the plates in meters. A Farad is a very large quantity of capacitance, so we will use metric prefixes to produce more usable numbers. Capacitance is normally measured in microfarads (μF), which is 1.0x10-^6 F, or picofarads (pF), which is 1.0x10-^12 F. 1.0F = 1,000,000μF = 1,000,000,000,000pF! Be very careful with your calculations! This calculation will give you an approximation of the capacitance of the lab capacitor. However, there are other factors that introduce errors into the real-world measurement of capacitance and voltage. You need to be careful to take these factors into account. Lab Equipment: To get good results, this lab activity requires some specialized equipment. You need a good regulated DC (direct current) power supply so that the voltage applied to the capacitor is the same in each trial. A battery would work but voltage applied changes over time. You also need a very accurate way of measuring the voltage between the plates without putting a resistive load on the capacitor. The amount of charge stored is very small, so a conventional voltmeter will not work. The minute charge built up in the capacitor would simply discharge through the meter, rendering any measurement useless. You will use a special voltage-measuring device called an Electrometer that measures voltage without discharging the capacitor. One problem with the electrometer is that it has some capacitance of its own. Since this capacitance is in parallel with that of the capacitor, the built-in capacitance of the leads must be added to that of the capacitor. Purpose: The purpose of this lab is to investigate the relationship between plate separation and voltage in a parallel plate capacitor kept at constant charge. Equipment: Variable capacitor Electrometer Regulated Power Supply
Cautions: This equipment is delicate. Everything should go together with the lightest of touches. Do not force anything! Your first task is to predict what will happen to the capacitor’s voltage when you charge it with a 15V source and then spread the plates apart (which reduces the capacitance). You will do this in the next section. Theoretical Calculations: You need to calculate the theoretical capacitance for each plate spacing. Here is the first one as an example. The hardest part of this is getting the units right. The easiest way to proceed is to put everything in meters for the calculations:
D. The formula for the energy stored in a capacitor is Ue=½CV^2. Does the energy stored in the capacitor remain constant when the plate spacing is varied? Does it go up or down? Discuss where the energy came from or went to.