Lab-03_Capacitors and Capacitance_updated

.pdf

School

University of North Carolina, Chapel Hill *

*We aren’t endorsed by this school

Course

2102

Subject

Electrical Engineering

Date

Apr 3, 2024

Type

pdf

Pages

10

Uploaded by mkidwai9248

Report
Fall 2021 1 Phys 2102 -Spring Spring 2023 LAB 3 PROPERTIES OF CAPACITORS Instructions: Use colors other than black while typing your answers so that it is easy for the graders/instructors to find your response. Lab Objectives Determine the ‘capacitance’ of a capacitor as a function of the plate size, gap & voltage between the plates. You will explore how changing the size of a capacitor changes the magnitude of charge stored by measuring (checking) the electric field between the plates. You will collect data from the PhET simulations . Introduction: Capacitors are the devices that store the charge and thereby electrical energy. These are made from two pieces of conductors separated by a small gap. One side (plate) is connected to the positive terminal of a battery, while the other side is connected to the opposite side (negative terminal) of the battery. Equal and opposite charges appear (store) on each plate. The amount of charge stored in each plate is given by: Q = C Δ V , where C is the capacitance and Δ V is the potential difference between the plates. The capacitance of a parallel plate capacitor is given by: 𝐶 = 𝜅𝜀 0 𝐴 𝑑 . Here, 𝜅 = dielectric constant, 𝐴 = area of each plate, 𝑑 = gap between the plates, 𝜀 0 = permittivity constant of empty space. The electric field E generated in a parallel plate capacitor is uniform. The energy stored is given by the equation, ? = 1 2 𝐶 ∆? 2 . The gap could be air, or any other dielectric material (insulator). The SI unit of capacitance is Farad (F). The unit ‘F’ is a ve ry large quantity and most capacitors are in the range of micro- Farad (μF), nano -Farad (nF) or pico-Farad (pF). 1. Properties of a Parallel Plate Capacitor: Open the Capacitor Lab: Basics https://phet.colorado.edu/sims/html/capacitor-lab-basics/latest/capacitor-lab-basics_en.html Select “Capacitance”. Take a few minutes to get familiar with this simulation. 1a. Make sure that all the boxes are checked:
Fall 2021 2 Phys 2102 -Spring Spring 2023 From the left box select: “Capacitance”, “Top plate charge”, “Stored Energy”. From the right box select: “Plate Charges”, “Bar Graphs”, “Electric Field”, and “Current Direction”) 1b. Bring in the voltmeter and connect its red probe to positive terminal and black probe to negative terminal of the battery. Note that the battery voltage and the voltage across the capacitor will have the same value when connected properly. (You can check it by dragging the yellow bar on the battery to a non-zero value and moving the voltmeter probe around the circuit). The battery should stay connected to the capacitor for this part of the lab. Fill in the following table: Table 1a: Capacitance, Charge on the Plate as a function of the Voltage across the Capacitor: (Drag the diagonal and vertical green arrow respectively to change area and separation values). Area 𝐴 = 400 ?? 2 ; Separation 𝑑 = 10 ?? ; Completely fill the Table with correct data [8 points] Battery Voltage ? (?????) Plate Charge 𝑄 (?𝐶) Capacitance 𝐶 (??) Stored Energy ? (?𝐽) 0 V 0 .3 0 0.25 V .07 .3 .01 0.5 V .15 .3 .04 1.0 V .3 .3 .15 1.25 V .37 .3 .23 1.5 V .44 .3 .33 1c. Plot a graph of the Plate Charge 𝑸 vs. Voltage 𝑽 in Excel and paste the graph below (Label the axes along with units to get full credit. You also need to perform a linear fit.) [5 Points] [Helpful video: https://www.youtube.com/watch?v=Xn7Sd5Uu42A ]
Fall 2021 3 Phys 2102 -Spring Spring 2023 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Plate Charge Voltage Voltage vs Plate Charge
Fall 2021 4 Phys 2102 -Spring Spring 2023 1d . Set the battery voltage to 1.5 V. Change the area of the capacitor. Fill in the following data table. Table 1b: Capacitance, Charge on the plate as function of the size of the capacitor: Completely filled Table with correct data [8 points] Area 𝐴 (?? 2 ) Gap 𝑑 (??) Plate Charge 𝑄 (?𝐶) Capacitance 𝐶 (??) 400 10.0 .53 .35 200 10.0 .27 .18 100 10.0 .13 .09 400 5 1.06 .71 400 2 2.66 1.77 1e. Based on the data of Table 1a, Table 1b and the plot, answer the following: (i) What is the relationship between the Charge 𝑄 and the Voltage ? across the capacitor? [3 Points] When voltage times capacitor equals plate charge. (ii) Does the capacitance of a capacitor depend upon stored charge 𝑄 and the voltage ?? If not, then what does the capacitance depend upon? Explain your answer. ( Hint: pay attention to the data of the tables ) [ 3 points] No it does not, it depends on the size of the plate and the distance between the plates.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help