Capacitance and Rc Circuits

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An Investigation on Capacitance and RC circuit
Hamdy Hamdy Abdel Moneim Abdou, Jaime Lorenzo C. Olivares, and Karol Giuseppe A. Jubilo National Institute of Physics, University of the Philippines, Diliman, Quezon City

Abstract
This experiment is designed to further the understanding of the relationship between voltage, charge, and capacitance of capacitors. This also explains how values of effective capacitance for series and parallel combinations of capacitors are obtained using effective equations. Accurate observations and results from devices such as the Labquest with a volt probe were used in the measurement of the voltage passing through the system in the calculations for the effective capacitances and the time constant of the capacitors. The theoretical and experimental data were used in the measurement of the percent error of the acquired values. It is anticipated that this paper will be consistent with the intuition of the students and serve as a reference for problems concerning the analysis of capacitors and RC circuits.

1. Introduction
A capacitor is a device that stores energy in the form of an electric field and can release that energy when necessary. Since capacitors can be made in more complex forms, the simplest form of capacitors, the parallel plate capacitor, was used in this experiment for simplification purposes. It works by insulating two metal plates and isolating them from each other using a dielectric material. When the capacitor is connected to a power supply, positive charges will collect in one of the plates, corresponding to an equal collection of negative charges in the opposite plate. This results in an electric field formed in between the two plates, with a corresponding charge equal to the absolute value of the charge collected in one of the plates. The maximum amount of energy a capacitor can contain is called the capacitance, and this is given by C = Q/V, where Q is the total charge in the capacitor and V is the potential difference of the capacitor. Capacitors can also be arranged in series and parallel. A series combination of capacitors would mean the charge is constant while the total voltage is the sum of the voltages passing through each capacitor while the parallel combination of capacitors would mean the charge is the sum of the charges in each capacitor and voltage remains constant. As such, the theoretical effective capacitance of a series combination would be given by Ceff = (1/C1 + …)-1 while the effective capacitance of a parallel combination would be given by Ceff = C1 + … The time it takes for the capacitor to charge is also a constant, meaning it is equivalent to the time it takes for the capacitor to discharge the energy stored. Due to the nature of capacitors, it also takes a very short time for a capacitor to charge and discharge, therefore a Resistor-Capacitor circuit, which is a circuit where a capacitor is connected to a resistor, is used. The reasoning behind this is that the resistor will slow down the flow of energy in the circuit, which will mean that time it takes for the capacitor to charge will increase. However, capacitors charge at an exponential rate, which means that theoretically it would take an infinite amount of time for capacitors to be fully charged, and it is given by the equation q = Qf(1-e-t/RC). If we graph the relationship the charge to time, we would see that it would be exponentially increasing when charging the capacitor and exponentially decreasing when discharging the capacitor. Also, if we graph the current versus time, the current would be exponentially decreasing when charging the capacitor, and negative but exponentially increasing when discharging the capacitor. This is because the current will decrease as less charges are being sent through the capacitor as it charges, but when the capacitor discharges, it would be a backward current, resulting in a negative current which...
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