02_Capacitors_Lab (Fall 2023)

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Electrical Engineering

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Apr 3, 2024

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1 Summer 2020 Capacitors Capacitors OBJECTIVE In this experiment, you will investigate fundamental properties of capacitors. A capacitor is a device that stores charge. THEORY A capacitor is used to store charge. A capacitor can be made with any two conductors kept insulated from each other. If the conductors are connected to source providing a potential difference V (e.g., to the opposite terminals of a battery), then the two conductors are charged with equal but opposite amount of charge Q, which is then referred to as the “charge in the capacitor.” The actual net charge on the capacitor is zero. The capacitance of the device is defined as the amount of charge Q stored in each conductor after a potential difference V is applied: 𝐶 = 𝑄 𝑉 Rearranging gives: 𝑉 = 𝑄/𝐶 (1) The simplest form of a capacitor consists of two parallel conducting plates, each with area A , separated by a distance d . The charge is uniformly distributed on the surface of the plates. The capacitance of the parallel-plate capacitor is given by: 𝐶 = 𝜘𝜀 0 𝐴 𝑑 (2) Where κ is the dielectric constant of the insulating material between the plates (κ = 1 for a vacuum; other values are measured experimentally and can be found in tables), and ε o is the permittivity constant, of universal value ε o = 8.85 x 10 -12 F/m. The SI unit of capacitance is the Farad (F). Any material placed between the plates of a capacitor will increase its capacitance by a factor κ, hence we have: C = κC o (3) with C o being the capacitance when there is a vacuum between the plates of the capacitor. Dielectric materials are non-conductive. Any dielectric material can be used to keep the plates in a capacitor insulated from each other (preventing them from touching and d ischarging). To three significant figures, κ = 1.00 for air. For all materials, κ > 1. If the charge on a capacitor is kept constant while a dielectric is inserted between the plates, Equations 1 & 3 yield: Q = CV = C o V o κC o V = C o V o so 𝑉 = 𝑉 𝑜 𝜘 (4) Where V 0 is the voltage before inserting the dielectric and V is the voltage after insertion.
2 Summer 2020 Capacitors Note that the magnitude of the electric field (E) between the plates of the capacitor is related to the voltage (V) across the plates and the separation distance (d) as given by: E = V/d (5) Finally, the energy stored in a capacitor (U) can be expressed in three ways: U = 1 2 𝑄𝑉 = 1 2 𝐶𝑉 2 = 1 2 𝑄 𝐶 2 (6) The energy is in Joules (J) for a charge in coulombs, voltage in volts, and capacitance in farads.
3 Summer 2020 Capacitors C APACITORS LAB REPORT Name(s): Nicole Munoz, Sophia Mar, Isabella Garza, Martina Rey, and Ana Irene Caarbajal GOAL: (briefly state what experiment(s) will be performed and with what purpose) This experiment explores the fundamental properties of capacitors, which store electrical charge using insulated conductors. When it is connected to a potential difference, equal but opposite charges accumulate on the conductor, which creates a charge in the capacitor. The net charge remains at 0, disregarding the accumulated charge. This experiment allows for a better understanding of the capacitor’s behaviors under different conditions, therefore improving our knowledge of fundamental electrical principles and drawing conclusions about their applications when using electrical circuits. PROCEDURE 1. Properties of a capacitor. In this experiment you will use a Java simulation to investigate fundamental properties of a parallel plate capacitor. Find the simulation on the PhET site: https://phet.colorado.edu/en/simulation/legacy/capacitor-lab . Another link: (If link above does not work) https://phet.colorado.edu/sims/cheerpj/capacitor-lab/latest/capacitor- lab.html?simulation=capacitor-lab After the applet starts, you should see the following window. Using the right-bottom corner of the window you can enlarge the window, for better visibility. A. Charging a capacitor. Disconnect Battery (by clicking on the control). Uncheck Plate Charges. Check Voltmeter. Attach the red probe to the top plate and the black one to the bottom plate. Slide the slider on the battery all the way down . Connect the battery. Now you should see the following picture. Check the electric field lines box. In the space below, draw the capacitor and show some electric field lines inside it.
4 Summer 2020 Capacitors Question 1. What is the polarity of the charges on the top plate of the capacitor? The top of the plate of the capacitor will be more negatively charged than the bottom. Check in the View on Plate Charges and check your answer.
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