With this mantra success is sure to come your way. At APEX INSTITUTE we strive our best to realize the Alchemist's dream of turning 'base metal' into 'gold'.
With this mantra success is sure to come your way. At APEX INSTITUTE we strive our best to realize the Alchemist's dream of turning 'base metal' into 'gold'.
Capacitors are geometries that can hold charges.
Use Gauss’ Law symmetries to calculate capacitance.
Series and parallel connections.
Dielectrics increase capacitance.
Capacitors Presentation
Presentations about capacitors
What is capacitor
Construction of capacitor
by Mudasir Nadeem
Institute of Chemical Sciences BZU Multan
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
Capacitors are geometries that can hold charges.
Use Gauss’ Law symmetries to calculate capacitance.
Series and parallel connections.
Dielectrics increase capacitance.
Capacitors Presentation
Presentations about capacitors
What is capacitor
Construction of capacitor
by Mudasir Nadeem
Institute of Chemical Sciences BZU Multan
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
ESC Beyond Borders _From EU to You_ InfoPack general.pdf
Capacitors
1. Lecture 5 Capacitance Chp. 26
•Cartoon - Capacitance definition and examples.
•Opening Demo - Discharge a capacitor
•Warm-up problem
•Physlet
•Topics
•Demos
• Circular parallel plate capacitior
•Cylindrical capacitor
•Concentric spherical capacitor
•Leyden jar capacitor
•Dielectric Slab sliding into demo
•Show how to calibrate electroscope
2. Capacitance
• Definition of capacitance
A capacitor is a useful device in electrical circuits that allows us to
store charge and electrical energy in a controllable way. The simplest to
understand consists of two parallel conducting plates of area A
separated by a narrow air gap d. If charge +Q is placed on one plate,
and -Q on the other, the potential difference between them is V, and
then the capacitance is defined as C=Q/V. The SI unit is C/V, which is
called the Farad, named after the famous and creative scientist Michael
Faraday from the early 1800’s.
• Applications
– Radio tuner circuit uses variable capacitor
– Blocks DC voltages in ac circuits
– Act as switches in computer circuits
– Triggers the flash bulb in a camera
– Converts AC to DC in a filter circuit
4. Electric Field of Parallel Plate Capacitor
E
0
q 0EA
Gauss Law
E
q
0A
q
A
A
qS
ES
V
0
Area A
+++++++++++
--------------------
E
+ q
- q
S
S
A
q
V
q
C
A
qS
0
0
Coulomb/Volt = Farad
5. Circular parallel plate capacitor
r r
s
r = 10 cm
A = r2 = (.1)2
A = .03 m 2
S = 1 mm = .001 m
S
A
C
0
F
C 10
10
3
pF
C 300
001
.
03
.
)
10
( 11
C Farad
Volt
Coulomb
p = pico = 10-12
Show Demo Model, calculate its capacitance , and show
how to charge it up with a battery.
6. Demo Continued
Demonstrate
1. As S increases, voltage increases.
2. As S increases, capacitance decreases.
3. As S increases, E0 and q are constant.
7. Dielectrics
• A dielectric is any material that is not a conductor, but polarizes
well. Even though they don’t conduct they are electrically active.
– Examples. Stressed plastic or piezo-electric crystal will produce a
spark.
– When you put a dielectric in a uniform electric field (like in between
the plates of a capacitor), a dipole moment is induced on the
molecules throughout the volume. This produces a volume
polarization that is just the sum of the effects of all the dipole
moments. If we put it in between the plates of a capacitor, the
surface charge densities due to the dipoles act to reduce the electric
field in the capacitor.
8. Dielectrics
• The amount that the field is reduced defines the dielectric
constant from the formula E = E0 / , where E is the new field
and E0 is the old field without he dielectric.
• Since the electric field is reduced and hence the voltage
difference is reduced (since E = Vd), the capacitance is
increased.
– C = Q / V = Q / (V0 / ) = C0
– is typically between 2 – 6 with water equal to 80
– Show demo dielectric slab sliding in between plates. Watch how
capacitance and voltage change. Also show aluminum slab.
11. Find the capacitance of a ordinary piece of coaxial cable (TV cable)
metal braid
with - q
outer insulator
•
signal
wire
radius a
with + q
Insulator
(dielectric )
radius b
a = 0.5 mm
b = 2.0 mm
2
For a long wire we found that
where r is radial to the wire. • r
a
b
Va is higher than Vb
L
Q
air
38
.
1
10
6
4
ln
10
6 11
11
L
C
m
PF
L
C
43
m
PF
L
C
86
0 (air)
= 2
ds = - dr because path of integration is radially inward
or
12. Model of coaxial cable for calculation of capacitance
Signal wire
Outer metal braid
13. Spherical capacitor or sphere
Recall our favorite example for E and V is spherical symmetry
Q
R
The potential of a charged sphere is V = (kQ)/R with V = 0 at r =
.
The capacitance is
R
k
R
R
kQ
Q
V
Q
C 0
4
Where is the other plate (conducting shell)?
It’s at infinity where it belongs, since that’s where the electric lines of flux terminate.
k = 1010 and R in meters we have
PF
cm
R
C )
(
Earth: C = (6x108 cm)PF = 600
F
Marble: 1 PF
Basketball: 15 PF
You: 30 PF
Demo: Leyden jar capacitor
Demo: Show how you measured capacitance of electroscope
14. Capacitance of two concentric spherical shells
+q
- q
ds = - dr
Integration path
E
a
b
15. Electric Potential Energy of Capacitor
• As we begin charging a capacitor, there is initially no potential difference between
the plates. As we remove charge from one plate and put it on the other, there is
almost no energy cost. As it charges up, this changes.
+ -
+q -q
At some point during the charging, we
have a charge q on the positive plate.
The potential difference between the plates is V = q/C. As
we transfer an amount dq of positive charge from the
negative plate to the positive one, its potential energy
increases by an amount dU.
.
dq
C
q
Vdq
dU
The total potential energy increase is
C
Q
C
q
dq
C
q
U
Q
2
2
2
2
0
Also C
Q
CV
QV
U
2
2
2
1
2
1
2
1
using C = Q/ V
16. Graphical interpretation of integration
Q
Vdq
U
0
where V = q/C
Q
dq
q/c
q
V
V = q/c
N
i
i
i q
q
C
U
1
1
= Area under the triangle
Area under the triangle is the value of the integral dq
C
q
Q
0
Area of the triangle is also = 1/2 bh
C
Q
q
dq
C
q
Q
2
2
2
2
0
Q
0
17. Where is the energy stored in a capacitor?
• Find energy density for parallel plate capacitor. When we charge a
capacitor we are creating an electric field. We can think of the work
done as the energy needed to create that electric field. For the
parallel plate capacitor the field is constant throughout, so we can
evaluate it in terms of electric field E easily.
Use U = (1/2)QV
A
Q
E
0
and V = ES
We are now
including dielectric
effects:
Solve for Q = AE, V = ES and substitute in
)
(
2
1
)
)(
(
2
1
2
1 2
AS
E
ES
AE
QV
U
volume occupied by E
2
2
1
E
AS
U
2
2
1
E
Electrostatic energy density general result for all
geometries.
To get total energy you need to integrate over volume.
18. How much energy is stored in the Earth’s atmospheric
electric field?
(Order of magnitude estimate)
atmosphere
h
R
Earth
20 km
R = 6x106 m
2
10
100
m
V
E
Volume
E
U
2
0
2
1
h
R
Volume 2
4
3
18
4
2
6
10
6
.
8
)
10
2
(
)
10
6
(
4 m
Volume
)
10
6
.
8
)(
10
)(
10
(
2
1 18
2
11
U
J
U 11
10
3
.
4
This energy is renewed daily by the sun. Is this a lot?
The total solar influx is 200 Watts/m2
day
J
s
J
Usun
21
16
6
10
2
10
2
)
10
6
(
14
.
3
200
10
10
2
sun
U
U
Only an infinitesimal fraction gets converted to electricity.
World consumes
about 1018 J/day.
This is 1/2000 of
the solar flux.
19. Parallel Combination of Capacitors
Typical electric circuits have several capacitors in them. How do they
combine for simple arrangements? Let us consider two in parallel.
V
C1 C2
+
-
Q1 Q2
V
C1
+
-
C = Q/V
We wish to find one equivalent capacitor to replace C1 and C2.
Let’s call it C.
The important thing to note is that the voltage across each is the
same and equivalent to V. Also note what is the total charge
stored by the capacitors? Q.
V
C
C
V
C
V
C
Q
Q
Q )
( 2
1
2
1
2
1
2
1
2
1 C
C
C
C
C
V
Q
20. Series Combination of Capacitors
C2
V2
C1
V1
+
-
+ - + -
Q Q
V C
V
+
-
+ -
Q
V
V
Q
C
C
Q
V
What is the equivalent capacitor C?
Voltage across each capacitor does not have to be the same.
The charges on each plate have to be equal and opposite in sign by
charge conservation.
The total voltage across each pair is:
)
1
(
)
1
1
(
2
1
2
1
2
1
C
Q
C
C
Q
C
Q
C
Q
V
V
V
So
2
1
1
1
1
1
C
C
C
; Therefore,
2
1
2
1
C
C
C
C
C
21. Sample problem
V
C1
C2
+
-
C3
C1 = 10 F
C2 = 5.0 F
C3 = 4.0 F
a) Find the equivalent capacitance of the entire combination.
C1 and C2 are in series.
2
1
2
1
12
2
1
12
1
1
1
C
C
C
C
C
C
C
C
F
C
3
.
3
15
50
5
10
5
10
12
C12 and C3 are in parallel.
F
C
C
Ceq
3
.
7
0
.
4
3
.
3
3
12
22. Sample problem (continued)
V
C1
C2
+
-
C3
C1 = 10 F
C2 = 5.0 F
C3 = 4.0 F
b) If V = 100 volts, what is the charge Q3 on C3?
C = Q/V
100
10
0
.
4 6
3
3
V
C
Q
c) What is the total energy stored in the circuit?
Coulombs
Q 4
3 10
0
.
4
J
V
C
U eq
2
4
6
2
10
6
.
3
10
10
3
.
1
2
1
2
1
J
U 2
10
6
.
3
23. Warm up set 5
1. HRW6 26.TB.03. [119752] A capacitor C "has a charge Q". The actual charges on its plates are:
Q/2, Q/2
Q, -Q
Q/2, -Q/2
Q, 0
Q, Q
2. HRW6 26.TB.13. [119762] Pulling the plates of an isolated charged capacitor apart:
increases the potential difference
increases the capacitance
does not affect the capacitance
decreases the potential difference
does not affect the potential difference
3. HRW6 26.TB.25. [119774] Let Q denote charge, V denote potential difference and U denote stored energy.
Of these quantities, capacitors in series must have the same:
Q only
Q and U only
U only
V and U only
V only
24. What is the electric field in a sphere of uniform
distribution of positive charge. (nucleus of protons)
R
r E