Find the voltage δv1 across the first capacitor

Physics 2 Lab 3 Report

Lab 3 is an experiment done on Capacitance & Capacitors:

I want about 4 to 5 pages well written report

The format should be:-

Introduction:

data: data is already collected and uploaded as an excel file so no need to write anything in here except mentioning that data is attached

data Analysis: here where all the calculations and errors are mentioned

Discussion: Which have two parts

Physics of the experiment: includes the physics behind the experiment

Sources of errors: here where it should mention the types of errors accrued and there affect

Conclusion:

Files attached:

An example of the report is attached (Phy2 lab3 (1).pdf) The first page leave it as it is

The procedure steps are attached (03 Capacitance & Capacitors.pdf)

Video of the experiment is attached in this link (https://fit.hosted.panopto.com/Panopto/Pages/Sessions/List.aspx#folderID=%22f90f2d96-a93f-4518-ad72-abc9005b20e1%22)

What is required to be mentioned in the report is attached (03 Guide.pdf)

The data sheet is attached (Phy 2 - Capictance and Capacitors (1).xlsx)

some photos are also attached for more clear clear vision

Lab 3/03 Capacitance & Capacitors.pdf
Florida Institute of Technology © 2020 by J. Gering

Experiment 3 Capacitance and Capacitors

Introduction The purpose of this experiment is to become familiar with the behavior of capacitors in direct current circuits. This involves constructing circuits with capacitors arranged in series and parallel. Concepts All objects are capacitors to one degree or another. In other words, we can charge all objects by forcing electrically charged particles (usually electrons) onto their surface. So all objects have some capacity to store electric charge and electric energy. We measure this ability to store charge by the quantity capacitance.

Applying a greater electric potential (or its associated electric field) will force more charged particles onto an object. It is better to eliminate the effect voltage has on determining the storage capacity of an object. Hence, capacitance is defined as the amount of charge stored by the object divided by the value of the object’s voltage (its electric potential relative to zero Volts). It is assumed the stored charge is an excess or deficiency of electrons compared to the normal number of electrons in the atoms of the initially neutral object. The unit of capacitance is then Coulombs / Volt, which is named the Farad in honor of Michael Faraday.

Capacitance: charge stored per unit of potential difference. � (1)

Capacitors can take any shape. The textbook derives expressions for two concentric spheres, two co-axial cylinders and two flat, parallel plates. It is convenient to think of these objects as being made of metal but non-conducting materials can store charge too.

� � � Figure 1.

� � � Eqn. (2) Eqn. (3) Eqn. (4)

a b ba area: A

d

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Florida Institute of Technology © 2020 by J. Gering

In Eqns (2), (3) and (4), the object’s capacitance is the permittivity of empty space multiplied by a geometrical factor for each object. So an object’s electrical capacitance is purely determined by its size, geometry and the material between its surfaces.

The generic symbol for a capacitor is the edge-on view of a parallel plate capacitor. This is because nearly all capacitors use a parallel plate geometry. Spherical capacitors are very rare and the most common cylindrical, electrical component that has capacitance are the coaxial cables used for cable television and telecommunications.

! ! Figure 2. Capacitors in Series Figure 3. Capacitors in Parallel

Equations (2), (3) and (4) indicate a vacuum (empty space) exists between the spheres, cylinders or plates. However, practically, this is almost never the case. Usually air or some insulator fills the space between the charged surfaces of the capacitor. An electric field exists between these surfaces and can be imagined to flow through the air or insulator. (In reality the molecules of the material between the plates becomes polarized. However, that topic will not be addressed in this experiment.) The prefix dia means through or across. Hence, the insulator inside the capacitor is called a dielectric material. The a in dia is dropped due to the first vowel e in electric. Dielectrics increase the capacitance of a given capacitor and this increase is characterized by a constant, K. Not surprisingly, K is called the material’s dielectric constant (or sometimes its relative permittivity). See Eqn. (5).

� (5) Consider two capacitors with different capacitances connected sequentially (in series). The wire connecting C1 and C2 contains many moles of free electrons. As the power supply pushes charged particles onto one of C1’s plates, the free charge on the other plate redistributes quickly to match. If +5 µC of charge collect on the one of C1’s plates, then C1’s other plate will almost instantly acquire -5 µC of charge. Furthermore, the wire connecting C1 to C2 will transfer the very same imbalance to the second capacitor. So for capacitors in series, Q1 = Q2 = Q3 and so forth. From the previous experiment, we know metal represents an equipotential surface. So

C1

C2

Vsupply

C1 C2

Vsupply

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Florida Institute of Technology © 2020 by J. Gering

even though the potential difference across each individual capacitor will be different, the potential difference between any two plates wired together must be equal. So for capacitors in series, ΔVpower supply = ΔV1 + ΔV2 +...

When capacitors are connected in parallel with each other, the situation reverses. Now, the potential difference across different capacitors are all equal and the stored charge must add sequentially to give the total charge stored on the equivalent (or total) capacitance. So for capacitors in parallel: Qtotal = Q1 + Q2 +... and ΔVpower supply = ΔV1 = ΔV2 = ...

The textbook combines the ideas in the preceding two paragraphs to derive the equations for the equivalent capacitance for capacitors in series and in parallel. See Equations (6) and (7). It turns out there is an exact analogy between capacitors arranged in this manner and mechanical springs connected in series and parallel. The analogy is exact because both capacitors and springs store potential energy and the equations that govern this energy have exactly the same form: Uelastic = ½ kx2 and Uelectric = ½ CV2. Similarly, Hooke’s Law and Eqn. (1) are equivalent in form: F = kx and Q = CV.

� � Eqn. (6) Eqn. (7)

Method

In this experiment, some of the circuits are built on a breadboard. A breadboard is a piece of molded plastic, which has been drilled with hundreds of small holes arranged in horizontal rows and vertical columns. Electrically, each hole is a jack because a thin, solid-conductor wire (stripped of its insulation) can be inserted into each hole. Beneath the hole is a spring-loaded, metal clip that holds the wire securely. The breadboard consists of the drilled piece of plastic, an insulated backing and rows and rows of interconnected metal clips embedded into the plastic.

There is a long gulley or trough cut down the center of the breadboard. Electrically, it separates the left and right hand rows of jacks. It also has a characteristic width so that integrated circuit chips can be inserted into the breadboard. Usually, the body of chip straddles the trough and the metal “legs” that stick out from the side of the chip push into the jacks immediately to the left and right of the trough. Figure 4 gives a schematic diagram of a breadboard showing how the jacks are interconnected inside the plastic. Figure 5 gives a photograph of the back side of a breadboard after the insulating backing has been removed.

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Florida Institute of Technology © 2020 by J. Gering

�

Figure 4. Schematic of breadboard showing hidden electrical connections inside the plastic

� Figure 5. Photograph of the reverse of a breadboard with its insulating back removed.

Parts 2 and 3 of the experiment utilize the PASCO Basic Electrostatics System. The apparatus consists of two wire cages one inside the other, one wand with a black plastic handle, a high voltage / low current power supply and a special meter for measuring voltages.

The Electrometer: At first glance, the electrometer looks like a cheap voltmeter. However ordinary voltmeters measure the electric potential energy of charged particles by siphoning off a

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Florida Institute of Technology © 2020 by J. Gering

small number of the charged particles being measured. This distorts the very thing you are trying to measure. One way to compensate, is to siphon off as little as possible. To do this the instrument must have a very high internal resistance so very little electrical charge gets drained away from the object under study. Common voltmeters have an internal resistance of 107 Ohms. This sounds high but it isn’t high enough for electrostatics experiments. The electrometer has an internal resistance of 1014 Ohms. So it will siphon off a current of only pico-Amps instead of the micro-Amps an ordinary voltmeter will require. The electrometer is powered by four AA batteries. It is a good idea to check these batteries once during the experiment to make sure none of them are leaking and causing corrosion in the electrometer.

Electrostatic Voltage Source (EVS): This is our ‘power supply’ for this part. But so little power is being supplied it is better to view it as a charging device. Through the marvels of modern semiconductor technology, this device can supply 1,000, 2,000 and 3,000 Volts (Joules of potential energy per Coulomb of charge) while limiting the maximum current to no more than 8.3 micro-Amps. Ordinarily thousands of Volts are extremely hazardous. But with this level of current limiting, you can touch bare wires energized to these voltages and not feel even a tingle. So this power supply is very safe despite its high voltage rating. The EVS has solid-state circuitry powered by an AC/DC adapter. Be sure to turn it OFF at the end of the experiment. Also do not let the wires connected to the EVS come into contact as a small spark will result.

The Wand: It has a black plastic handle and a special white insulating neck near the disk. The white material is a polycarbonate with an electrical resistance of 1014 Ohms. The wand has an aluminum covered disk. The disk below the aluminum is black polycarbonate mixed with carbon. This provides a moderate conductor (resistance is 1,000 Ohms) capable of storing charge with a very good conducting surface. This wand is used for transferring charge. For good results you must keep the disk clean. When not in use, place it in its plastic sleeve. You can clean the disk with alcohol and soft paper towel.

The Faraday Ice Pail: This is the two cylindrical wire cages. The outer cage is a shield which prevents stray charges from affecting the charged inner cylinder. The inner cylinder is called the pail. It is your bucket for holding electrically charged particles. The pail is insulated from the base but the shield is in contact with the base. So the shield and base are effectively grounded due to contact with the table top. Michael Faraday used a metal ice pail for his experiments in electrostatics. A solid metal bucket would work here but the wire cages let you see inside.

Important: Throughout the last part, the relative charged state of the aluminum disk on the wand is determined by the electrometer. When the disk touches the capacitor plate it picks up some charge. When the disk is placed inside the inner cage of the Faraday Ice Pail, the charge on the disk reorganizes the free charge on the inner cage and the electrometer measures a change in the electric potential energy per unit charge on this free charge in the inner wire cage. Electric potential energy per unit charge is called electric potential and is measured in the Joule / Coulomb, which is called a Volt. So, the electrometer measures an electric potential difference (a voltage), which ends up being proportional to the charge on the disk. 


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Procedure

Part 1 Capacitors in Series and Parallel

Important Note: Charged capacitors will discharge through the multimeter at a non-constant rate with respect to time. This discharge will be negligible if you make momentary contact with the multimeter’s leads and if the product of the capacitance and the internal resistance of the multimeter is a relatively large (~50 or more). The internal resistance of the multimeters is 107 Ohms. If you notice the multimeter’s readings change with time, you must use the electrometer to make the voltage measurements. Its internal resistance is 1014 Ohms.

1) Obtain three capacitors from the front table. Two of the capacitors can have the same value. Also obtain 8 or 9 thin wires with stripped ends. Make sure you have one or two long thin wires. Examine the stripped ends and ensure they are relatively straight and not too bent or curled. Usually, red insulation represents the positive input voltage and black represents ground. A suggestion is to use green for the connecting wires to denote intermediate values of voltage.

2) Consult the Method section of Experiment #2 to recall how to set the current limit on the D. C. power supply to 0.3 Amp. Set the voltage to 10 Volts and connect hook-up wires from the power supply to the red and black, banana-plug jacks on the breadboard. Unscrew the top part of the banana plug jacks and insert thin wires into the holes drilled into the binding post. Screw the top part back down to secure one end of the thin wire. Push the other end of the thin wires into small holes on the breadboard. Make certain the positive wire is electrically separated from the negative wire. It is probably best to run the positive wire to a row near the top of the breadboard and a very long, thin ground wire down toward the bottom of the breadboard.

3) Record the manufacturer’s rated capacitance of each capacitor. If not otherwise specified, assume the intrinsic random error in these values is ±20%.

4) Discharge each capacitor by momentarily clipping one wire to the capacitor’s leads. Obtain a digital capacitance meter and measure the capacitance of each capacitor. Be sure not to touch the alligator clips or the capacitor’s leads while making the measurement. Record the values.

5) Connect all three capacitors in series with the 10 Volt power supply. Note that some capacitors are polarized. Ask you instructor how to determine which lead you connect to the higher potential.

6) Set the multimeter to measure voltage. Then use the multimeter and probe across each capacitor. Grip banana plugs by the yellow plastic and not the metal. Assign an uncertainty to each measurement. Question: Do the voltages correctly sum to give the voltage of the power supply?

7) Compare voltage measurements across series capacitors when you probe momentarily with the leads versus leaving the leads connected to the capacitor for a minute or two.

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Florida Institute of Technology © 2020 by J. Gering

Question: Do you notice a difference? If there is a difference, explain why in your report.

8) Use Eqn. (1) to calculate the charge stored on each capacitor.

9) Calculate the equivalent capacitance of the circuit using the capacitances you measured in procedure (4).

10) Disconnect the circuit and discharge the capacitors. Connect the three capacitors in parallel with each other and then connect the capacitors to the power supply.

11) Again, use the multimeter to measure the voltage across the three capacitors connected in parallel. Do your measurements agree with your expectations from theory?

12) Again using Eqn. (1), calculate the charge stored on each capacitor.

Part 2 The Circular, Parallel Plate Capacitor

1) Turn on the capacitance meter. Connect red and black wires to the capacitance meter and push alligator clips onto each banana plug. Hold the banana plugs by their plastic part and have your partner record the capacitance reading. You must subtract this approximately constant value from whatever your read. Alternatively you can press the zero button before each reading however, there will always be a few fractions of a picoFarad of extraneous capacitance in the reading.

2) Clip the wires to the screw posts on the back of each plate’s mount. Vary the plate separation distance d from 7 or 8 centimeters down to a few millimeters and examine how the capacitance varies with plate separation distance.

3) Measure and record the diameter of one of the plates. Clean off finger prints and oils left behind with paper towel and either water or rubbing alcohol.

4) Set the separation distance to 3 mm and measure the capacitance. Subtract the capacitance value when nothing was connected to the wires.

5) Calculate the capacitance using C = εairA / d. The dielectric constant of air is κair = 1.00059 and the electrical permittivity is εair = κair ε0. Here, epsilon-zero is the permittivity of empty space (i.e. the vacuum): 8.85418782 × 10-12 m-3 kg-1 s4 A2.

6) Calculate the capacitance from the equation and compare it to the measured value by calculating a percent difference. Agreement to within 10 to 15% is acceptable.

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Florida Institute of Technology © 2020 by J. Gering

Part 3 Stored Charge and Capacitor Plate Separation

1) The mathematical definition of capacitance reads: C = Q / ΔV, where ΔV is the voltage applied across the two plates. Simultaneously, we have C = εairA / d. Combining these two equations predicts the charge Q stored on the plates should increase linearly as the distance between the plates d decreases.

a) Turn OFF and disconnect the capacitance meter. Separate the plates by 11.0 cm. Note, this means you must move one plate beyond the 10 cm scale printed on the apparatus. Also, be sure to sight along the plates; do NOT use the plastic markers on the base of the plate support. These markers do not refer to the true distance between the plates.

b) Connect the EVS to the plates and apply 3000 Volts. Connect the Faraday ice pail shield to ground on the EVS and connect the inner cage to the electrometer. Turn the electrometer on and select the 10 Volt range.

c) Use the aluminum covered wand (historically called a proof plane) to collect charge from the center of the plate being held at 3000 Volts. Keep the proof plane in place for 3 seconds. Then smoothly and quickly move it to the CENTER of the ice pail’s inner cage. DO NOT TOUCH THE PROOF PLANE TO THE INNER CAGE, otherwise damage may result to the electrometer. Keep body motions to a minimum and be consistent with how far you place the wand into the inner cage. This procedure may require some repeated trials.

d) In a data table, record the plate separation and the maximum potential on the inner cage: di and Vi. Remove the wand and ground the electrometer and proof plane. Reduce the plate separation by one centimeter and repeat the measurements to obtain di+1 and Vi+1. Continue reducing the plate separation by 1 cm increments and record the electrometer’s reading until the plate separation it is equal to 3.0 cm.

2) Use Excel to create a scatter plot of the ratio di / di+1 on the x-axis and the ratio Vi+1 / Vi on the y-axis. Yes, the indices are reversed intentionally. Perform linear regression on the data and display the slope and R2 (goodness-of-fit) parameter on the graph. An analysis of this part found below shows these two ratios are equal. Therefore, the slope of the best-fit line should be 1.0. Calculate a percent difference between the best-fit line’s slope and 1.0 to gauge the success of this part.

3) Turn off the EVS and the electrometer, disconnect wires, clean up your station and hang the wires on their racks. Return the capacitance meter to the front table. If you are in the very last section of lab that meets for the week, unscrew the back of the electrometer, remove the batteries and screw the back cover onto the electrometer.

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Florida Institute of Technology © 2020 by J. Gering

Theory Addendum

The capacitance of the capacitor is a constant as long as the applied voltage, plate area and plate separation remain constant. In this case, a constant total charge will be stored on the two plates. In this experiment, the applied voltage is provided by the EVS, which is set to 1000 Volts.

However, we are going to decrease the plate separation in steps. As we do so, the capacitance will increase and the connected EVS will force additional charge onto the plates. So at any one step we will have:

!

Every time the student samples the center of one plate with the wand (the proof plane), he/she removes a small amount of charge, ! which is proportional to the total charge stored on the plate. The EVS instantly replenished the charge on the plate. !

This small amount of charge is then measured by the Faraday Ice Pail and the electrometer. The electrometer’s reading is a small voltage that is assumed to be directly proportional to the charge on the proof plane. !

So we can rewrite the first equation as follows.

!

Using the relationship for a parallel plate capacitor we can write

!

And after the next time the plate is moved and the charge is sampled we have

!

Next we form the quotient of the last two proportions. The proportionality constants (whatever they are) will divide out giving

!

Dividing out common terms gives the equation we will graph

!

Since we are changing the distance between the plates, we plot that ratio on the x-axis (the independent variable).

C i = Q i

1000

δq i

δq i ∝Q

i

δq i ∝V

i

C i ∝ V i

1000

ε 0

A d i

∝ V i

1000

ε 0

A d i+1

∝ V i+1

1000

ε 0

A d i+1

ε 0

A d i

=

V i+1

1000 V i

1000

d i

d i+1

= V i+1

V i

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__MACOSX/Lab 3/._03 Capacitance & Capacitors.pdf
Lab 3/03 Guide.pdf
Experiment 03 Guide Capacitance and Capacitors

Videos

Improved videos are now available for Spring 2021. Navigate to Canvas > Pages > View All Pages > 03,… The newer videos are listed before a group of very short video clips. When viewed in alphabetical, filename order, the very short clips follow the procedure. In your data analysis section, provide a list that matches the video clip to the procedure number.

Part 1

Watch the Part 1 video to find the data for the first procedures of Part 1 where the capacitance of the capacitors are measured.

Part 2

The video contains one trial of measuring the voltages across the capacitors in series. Add these trials to what is in the video. Then analyze the data following the procedure. The voltages across the capacitors connected in parallel to each other will be 10 Volts. Comment on this in your report but no data analysis is needed.

Part 3 - Stored Charge and Plate Separation

Record the data from the Part 3 video and analyze the data according to the procedure. Discuss the success of this part. Question: Given what is in the video, could the procedure be modified to possibly obtain better results?

Vc (Volts) Vc (Volts) Vc (Volts) Vc (Volts)

Trial 1 Trial 2 Trial 3 Trial 4 Trial 5

upper cap 3.81 2 4.25 4.71

middle cap 3.34 3.6 3.58 3.21

lower cap 3.04 3.7 2.39 2.1

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__MACOSX/Lab 3/._03 Guide.pdf
Lab 3/03_2.jpg
__MACOSX/Lab 3/._03_2.jpg
Lab 3/03_3.jpg
__MACOSX/Lab 3/._03_3.jpg
Lab 3/03_4.jpg
__MACOSX/Lab 3/._03_4.jpg
Lab 3/Phy 2 - Capictance and Capacitors (1).xlsx
Sheet1
Phy 2 - Capictance and Capictors Aaron G. Talal M. 2/3/21
Series Capictance 10 Volts
Light Blue 10.88 uF Use equation 1 to solve for charge
Black 4.59 uF
Dark Blue 7.1 uF
Series Voltage Volts 10
Light Blue 2.7 V
Black 0.119 V
Dark Blue 6.4 V
Parallel Capcitance 10 volts
Light Blue 10.88 uF Use equation 1 to solve for charge
Black 4.59 uF
Dark Blue 7.1 uF
Parallel Voltage 10 volts
Black 9.79 V
Light Blue 9.79 V
Dark Blue 9.79 V
Diameter of plate 19.812 cm 0.19812 m
Capictance at 3 mm 1.5 V
Capictance at 11 cm 2.1 V
-0.6 V
-1.3 V
-2.6 V
-3.1 V
-3.9 V
-8.9 V
-9.9 V
__MACOSX/Lab 3/._Phy 2 - Capictance and Capacitors (1).xlsx
Lab 3/Phy2 lab3 (1).pdf
Experiment 3

Capacitance & Capacitors

By:

Talal Al Mahrizi

PHY 2092

Experiment Performed: 02/03/21

Report Submitted: 02/10/21

Lab Partner:

Aaron ​Glenore

Instructor:

Brandon Corea

Introduction

The goal of his experiment is to understand and be familiar with how capacitors behave

when connected to a direct current circuit. This is going to be by constructing circuits with

capacitors in both parallel and series. The capacitance, charge and the change in potential were

measured then compared to their theoretical values. No deviation from the lab manual occurred

when performing this experiment.

Data

Data is attached in the data sheet at the end

Data analysis

Part 1:

Series

C​expeimental

1Ctotal = 1 C1 +

1 C2 +

1 C3

= 110.84 + 1

7.1 + 1

4.59

= 2.2175

C​Theory

1Ctotal = 1 C1 +

1 C2 +

1 C3

= 110 + 1

6.8 + 1

4.7

= 2.1747

Percent difference

diff 100%% = Ctheory | Cexperimental − Ctheory |

*

00% 1.97 %= 2.1747 | 2.2175 − 2.1747 |

* 1 =

Parallel

C​expeimental

expeimental 1 C2 C3 C = C + +

= 22.53expeimental 0.84 7.1 4.59C = 1 + +

C​theory

theory 1 C2 C3 C = C + +

= 21.5theory 0 6.8 4.7C = 1 + +

Part 2

C​theory ​ = d Ɛ air A

C​theory ​ = 1.3781 10d Ɛ air r * 2 = 0.19812

1.00059 8.85418782 10 0.00981* * −12

* * = * −12

Discussion

Physics of Experiment:

Capacitance is the ability to store electrical energy in an object. Therefore, it is true to say

that almost all objects that can charge their surfaces by electrons are capacitors. In a

mathematical way, capacitance states that measuring the amount of charges per unit of potential

difference the capacitance can be calculated .The capacitance value of a capacitor is/ᐃV C = Q

measured in ​farads (F)​.

In a series circuit, Q in the source is the same throughout the circuits. The voltage is

splitted throughout the circuit ​sum up to the source voltage. TheV source V 1 V 2 ..., ᐃ = + + .

capacitance is ....1Ctotal = 1 C1 +

1 C2 + .

In a parallel circuit, Q is splitted throughout the circuit Qsource Q1 Q2 ..., ᐃ = + + .

sum up to the source charge. The voltage going out from the source is the same throughout the

circuits, the same voltage to all capacitors. The total capacitance is the sum of all capacitors

total C1 C2 ... C = + +

Sources of error:

Many equipment and devices were used in this experiment which caused several errors to

occur and affected the values gathered. There was a random error caused by inaccuracy while

setting the voltmeter to zero. There was also systematic intrinsic error caused by a change in the

values of V and calculation on C. This was caused because of the non-linear discharging of the

capacitors while they were used to measure the voltage. There was also an intrinsic random error

due to the changing while reading the voltage and capacitance.

Discussion questions:

1. Question: Do the voltage correctly sum to give the voltage of the power supply

It is proximity correct with a small error the summation came up to 9.219 which is less than the po

2. Question: Do you notice a difference? if there is a difference, explain why in your report.

The is some difference and this might be because the power supply gave a little

less accurate voltage or some the electricity may have moved out of the circuit

through the leads.

Conclusion:

The purpose of this experiment was to understand how capacitors work in s direct current

circuit. Also the way to set up capacitors and how voltage behaves in both series and parallel was

learned in this experiment. The separation of the two plates affected the capacitance between the

plates. The rule d < 𝞼 ​d ​, satisfied for all the cases which means the experiment wasn success. My

lab partner did a great job in this experiment.

__MACOSX/Lab 3/._Phy2 lab3 (1).pdf