Lab-03_Capacitors and Capacitance_updated
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Apr 3, 2024
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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.
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Related Questions
The given voltage should be proven the same in the solution. Thanks.
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i.
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ii.
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B. Combination of Capacitors (connect it with a battery and LED)
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2. Measure the equivalent effective capacitance of the combination.
3. Compute this theoretical value of capacitors in series using the formula
1_1, 1, 1
Crotat C* C*G,
4. Repeat steps 1 and 2 but this time connect the capacitors in parallel. Compute this
theoretical value of capacitance in parallel using the formula below.
Crotal = C + Cz + C,
5. Compute the percent error for both connections. Record all your observations and
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Table 2
Capacitor 1
Capacitor 2
Capacitor 3
Experimental capacitance (in series)
Experimental capacitance (in parallel)
Conclusions:
Questions:
1. How does the area of the aluminum foil affect the capacitance if the paper capacitor?
2. How does the thickness of the paper dielectric affect the capacitance of the paper
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3. Did you get the same capacitance using different types of paper? What do you think…
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d) Calculate the voltage across each capacitors in Figure Q1(d) during steady state.
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through the dielectric material. Include in the description relevant mathematical
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(b) A capacitor such as illustrated in Figure Q.3 is constructed using copper as plate
A and plate B plus a dielectric material with ɛ, 3.8 and o = 4 S/m between the
plates. Potential
difference
plates A
across
is VAB (t) =
Vo cos(2n x 10°t) V. Assume that Plate A and plate B carry charges +Q(t) and
and
-Q(t) respectively as well as fringing field at the edge of the plates can be ignored,
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(i)
Q(t) if the capacitance is 2.135 x 10-11 F
(ii)
M(t) if electric field within the capacitor, E(t) = M(t)
fV/m
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(iii) Conduction current density and conduction current.
UNIVE
(iv) Displacement current density and displacement current.
arch
ASUS VivoBook
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b) Write any four name of the practical types of capacitor?
c) How do you discharge the capacitor?
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Web/Home
F4
Search
F8
F9
c) Some capacitors are marked 45micro farad save working voltage 25V.
On a circuit diagram show how a number of these capacitors may be
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45 micro farads safe working voltage of 50 volts.
75 micro farads safe working voltage of 25 volts.
1.
I.
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