Capacitance :

Capacitance is the ability of a capacitor to store electric

charge. It is defined as the ratio of the electric charge on
each conductor to the potential difference between
them. Capacitance is measured in Farads (F) and
depends on the physical characteristics of the capacitor,
such as:
- Plate area
- Distance between plates
- Dielectric material

The formula for capacitance is:

C=Q/V

Where:
C = capacitance (in Farads)
Q = electric charge (in Coulombs)
V = potential difference (in Volts)

In essence, capacitance measures a capacitor's

capacity to store electric charge and energy.
Introduction To Capacitor :
A capacitor is an electronic component that stores
electrical energy in an electric field. It consists of two
conductive plates separated by a dielectric material.
When a voltage is applied, charge accumulates on the
plates. Capacitors are measured in Farads (F) and are
used for energy storage, filtering, and signal coupling.
They're crucial in electronic circuits, power supplies, and
audio equipment. Capacitors filter unwanted
frequencies, regulate power, and store energy. Different
types, such as ceramic, electrolytic, and film capacitors,
offer unique characteristics. Capacitors play a vital role
in modern electronics, enabling efficient energy storage
and signal processing. Their applications range from
simple filters to complex power systems, making them a
fundamental component in many devices. Capacitance
is a key concept in understanding electronic circuits.

A capacitor stores an electric field

by accumulating charge on its
plates when a voltage is applied.
The dielectric material between the
plates acts as an insulator,
allowing the electric field to be stored. The field's
strength depends on the voltage and plate separation.
The capacitor maintains the field as long as the voltage
is applied, enabling energy storage and signal filtering.
 Invention of capacitor:
The invention of the capacitor is attributed to several
individuals who contributed to its development over time.
Two key figures are:

1. Ewald Georg von Kleist (1700-1748): A German

physicist who independently discovered the principle of
the capacitor in 1745. He found that a glass jar coated
with metal foil on both the inside and outside could store
electric charge.

2. Pieter van Musschenbroek (1692-1761): A Dutch

physicist who also discovered the capacitor principle in
1746, around the same time as von Kleist. His
experiments led to the development of the Leyden jar,
an early form of capacitor.

The Leyden jar was a significant step in the

development of capacitors, and it paved the way for
further research and advancements in electrical storage
and circuitry. Over time, capacitors have evolved into
various types and are now essential components in
modern electronics
Amount of charge a Capacitor can
store:
The amount of charge Q a capacitor can store depends
on two major factors- the voltage applied and the
capacitor's physical characteristics, such as its size .
Electric field lines start on an individual positive and end
on a negative one, so that there will be more field lines if
there is more charge. The electric field strength is, thus,
directly proportional to Q.

The field is proportional to the charge: E ∝ Q

We know that V = Ed So, V∝E Hence, V∝Q Removing
sign of proportionality we get Q = CV
Where C = Capacitance of the Parallel Plate Capacitor.

The unit of capacitance is the farad (F), named after

Michael Faraday (1791-1867), an English scientist who
contributed to the fields of electromagnetism and
electrochemistry. Since capacitance is charge per unit
voltage, we see that a farad is a coulomb per volt.

(1C)/(1V) =1 F

A 1-farad capacitor would be able to store 1 coulomb

with the application of only 1 volt. is, thus a very large
capacitance. Typical capacitance ranges from fractions
of a picofarad to millifarads.
Working of Capacitor
A capacitor is an electronic component that stores
electrical energy in an electric field. It typically consists
of two conductive plates separated by a dielectric
material, which is an electrical insulator. When a voltage
is applied across the plates, one plate accumulates a
positive charge and the other a negative charge. This
charge separation creates an electric field within the
dielectric. The dielectric material is crucial as it
increases the capacitor's ability to store charge by
allowing for a stronger electric field to form between the
plates for a given voltage.
The amount of charge a capacitor can store per unit of
voltage is called its capacitance, measured in Farads
(F). When connected to a DC circuit, a capacitor will
charge until the voltage across its plates equals the
source voltage. Once charged, it acts as an open circuit,
blocking the flow of direct current. In an AC circuit,
however, a capacitor continuously charges and
discharges as the voltage alternates, effectively allowing
alternating current to pass through while impeding direct
current. This property makes capacitors vital in various
applications, including filtering, smoothing power
supplies, timing circuits, and energy storage.
Self-Capacitance
Self-capacitance property is related to the capacitors
especially to the isolated conductor to raise its potential
difference to one volt. Generally normal conductors will
have mutual capacitance. This is also measured in the
S.I units i.e. Farads.
The Self-capacitance of a conducting sphere which has
the radius 'R' is given by.
C=4πεοR
Self-capacitance values of some standard devices are
given below.
●​ For the top plate of a van de Graff generator which
has a radius of 20 cm, self-capacitance is 22.24pF.
●​ For the planet EARTH self-capacitance is 710 μF.

Principle of capacitor and its concept

Principle- It work on the principle of Induction of Charge
Consider a positively charged plate 1 and place an
uncharged plate 2 close to it. Due to induction, negative
charges on the second plate will gather towards the first
plate. This concentration of negative charges effectively
lowers the potential of the first plate for a given amount
of charge. Consequently, more positive charge can be
supplied to the first plate before its potential rises to the
level it would have reached without the presence of the
second plate.
Charging & Discharging of a
Capacitor

Let us assume that the capacitor, which is shown in the

Figure below in the circuit, is completely discharged. In
this circuit the capacitor value is 100 µF and the supply
voltage applied to this circuit is 12V.
Now the switch which is connected to the capacitor in
the circuit is moved to the point A.
Then the capacitor starts charging with the
charging current I.The charging voltage
across the capacitor is equal to the supply
voltage when the capacitor is fully charged
i.e. VS = VC = 12V.

In the case of ideal capacitors the charge remains

constant on the capacitor but in the case of general
capacitors the fully charged capacitor is slowly
discharged because of its leakage current.
When the switch is moved to the position B, then the
capacitor slowly discharges by switching on the lamp
which is connected in the circuit.
Types of Capacitors:
- Ceramic Capacitors:Small, inexpensive.
- Electrolytic Capacitors: High capacitance values, often
used in power supplies and audio equipment.
- Film Capacitors: Stable and reliable, used in
applications requiring high precision.
- Variable Capacitors: Capacitance can be adjusted,
used in tuning circuits.

Ceramic Capacitors
Ceramic capacitors are a type of fixed
capacitor that uses ceramic material as
the dielectric. They are known for their
compact size, low cost, and high.
capacitance values. Ceramic capacitors
are stable over a wide range of temperatures.
and frequencies, making them suitable.
for various applications.

Characteristics:
- High capacitance-to-volume ratio
- Low cost
- Stable over temperature and frequency
-Compact size
Applications:
- Decoupling and filtering: Ceramic capacitors are used
to filter out unwanted signals and decouple power
supplies.
- Bypass capacitors: They are used to bypass AC
signals around DC power supplies.
- High-frequency applications: Ceramic capacitors are
suitable for high-frequency applications due to their low
inductance and high-frequency stability.
- Electronic circuits: They are widely used in electronic
circuits, including consumer electronics, automotive, and
industrial applications.

Types:

- Class 1 ceramic capacitors: High-stability, low-loss

capacitors used in precision applications.
- Class 2 ceramic capacitors: High-capacitance,
general-purpose capacitors used in a wide range of
applications.

Overall, ceramic capacitors are a popular choice for

many electronic applications due to their reliability, small
size, and cost-effectiveness. They offer a range of
benefits and are widely used in various industries.
Electrolytic Capacitors
Electrolytic capacitors are a type
of capacitor that uses an electrolyte.
to achieve high capacitance values.
They are polarized, meaning they
have a positive and negative terminal, and are
commonly used in:

- Power supply filtering: Smoothing out voltage ripples

and noise.
- Audio equipment: Coupling and filtering audio signals.
- DC-DC converters: Filtering and regulating DC power.

Key Characteristics:
- High capacitance values: Electrolytic capacitors offer
high capacitance values in a relatively small package.
- Polarized: Must be connected correctly to avoid
damage or explosion.
- Limited lifespan: Electrolytic capacitors can degrade
over time due to electrolyte evaporation.

Types:
-Aluminum electrolytic capacitors: Most common
type,used in a wide range of applications.
- Tantalum electrolytic capacitors: Known for their high
reliability and stability.
Electrolytic capacitors are widely used in electronic
circuits due to their high capacitance values and
compact size. However, they require careful handling
and correct polarity to ensure reliable operation.

Film Capacitors
Film capacitors use a thin plastic film
as the dielectric material. They are known
for their:
- High stability and reliability
- Low ESR (Equivalent Series Resistance)
- High frequency stability, Self-healing properties.

Applications:
- Audio equipment: Film capacitors are used in audio
circuits for their high fidelity and low distortion.
- Power electronics: They are used in power supplies,
motor drives, and other high-power applications.
- High-frequency applications: Film capacitors are
suitable for high-frequency applications due to their low
ESR and high stability.

Types:
- Polyester film capacitors: General-purpose capacitors
with good stability and low cost.
- Polypropylene film capacitors: High-performance
capacitors with low ESR and high stability.
- Polyphenylene sulfide (PPS) film capacitors:
High-temperature capacitors with excellent stability and
reliability.
Applications Of Capacitor
Capacitors are incredibly versatile components with a
wide range of applications in electronics and electrical
systems. Here are some key uses:

* Energy Storage:

* Camera Flashes: Store energy quickly and release it

as a high-intensity burst for the flash.
* Power Supplies: Smooth out voltage fluctuations and
provide a stable DC output by storing and releasing
energy.
* UPS Systems: Act as temporary power sources
during brief outages, preventing data loss in devices.
* Motor Starting: Provide an initial surge of current to
start electric motors, especially in appliances like air
conditioners and washing machines.

* Filtering and Signal Processing:

* Decoupling: Reduce noise on power supply lines,
protecting sensitive components like microchips.
* AC Coupling/DC Blocking: Allow alternating current
(AC) signals to pass while blocking direct current (DC)
signals, essential in audio circuits and communication
systems.
 * High-Pass/Low-Pass Filters: Form part of filter
circuits to allow specific frequency ranges to pass or
block them, used in audio equalizers and radio tuning.
* Noise Suppression: Absorb and shunt unwanted
electrical noise in various circuits.

* Timing Circuits:
* Oscillators: Combine with resistors to create precise
time delays and generate oscillating signals in clocks,
timers, and signal generators.
* Timing Functions: Used in various control circuits
where specific time delays are required.

* Sensing:
* Touchscreens: Detect changes in capacitance when
a finger touches the screen.
* Proximity Sensors: Sense the presence or absence
of objects based on capacitance changes.
* Level Sensors: Measure fluid levels (e.g., fuel) by
detecting changes in capacitance.

* Power Factor Correction:

* Improve the efficiency of AC electrical systems by
compensating for reactive power, leading to reduced
energy losses.
Parallel Plate Capacitor:
A parallel plate capacitor is a type of capacitor
consisting of two parallel conductive plates separated by
a dielectric material. The plates are typically flat and
parallel to each other, with a uniform distance between
them. This design allows for a uniform electric field
between the plates, making it a fundamental component
in many electronic circuits.

Key Characteristics:

- Capacitance: Directly proportional to plate area and

inversely proportional to plate separation.
- Electric Field: Uniform between the plates, with
direction from positive to negative plate.
- Applications: Used in various electronic circuits,
including filtering, coupling, and energy storage.
The parallel plate capacitor is a simple yet essential
component, widely used in many applications due to its
predictable behavior and ease of design.
Spherical Capacitor:
A spherical capacitor consists of two concentric
spherical shells separated by a dielectric material. The
inner shell is typically charged to a certain potential,
while the outer shell is grounded. This design allows for
a unique distribution of electric field lines and
capacitance properties.

Key Characteristics:

- Capacitance: Depends on the radii of the inner and

outer spheres.
- Electric Field: Radial and symmetrical, decreasing with
distance from the center.

- Applications: Less common than parallel plate or

cylindrical capacitors, but used in specific applications
requiring symmetrical capacitance.

Spherical capacitors are often used in theoretical

calculations and specialized applications due to their
unique geometry and properties.
Cylindrical Capacitor:
A cylindrical capacitor consists of two coaxial cylindrical
shells separated by a dielectric material. The inner
cylinder is typically charged to a certain potential, while
the outer cylinder is grounded. This design allows for a
radial electric field and unique capacitance properties.

Key Characteristics:

- Capacitance: Depends on the length and radii of the

inner and outer cylinders.
- Electric Field: Radial and symmetrical, decreasing with
distance from the axis.

- Applications: Used in various applications, including

power transmission lines, capacitors in electrical
systems, and high-voltage applications.

Cylindrical capacitors are commonly used in situations

where a high capacitance per unit length is required,
and their design allows for efficient energy storage and
transmission.
Combination of Capacitors
1. Capacitors in Parallel

When capacitors are connected in parallel, their

individual capacitances add up to give a larger
equivalent capacitance.

Characteristics of Parallel Combination:

* Voltage: The voltage across each capacitor in a

parallel combination is the same and equal to the total
voltage applied across the combination.
* Charge: The total charge stored in the parallel
combination is the sum of the charges stored in each
individual capacitor.
* Effective Capacitance (Cp): The total capacitance is
the sum of the individual capacitances.
Formula for Parallel Capacitors:
For n capacitors (C1, C2, C3, ..., Cn) connected in
parallel, the equivalent capacitance is:
Cp = C1 + C2 + C3 + ... + Cn

Analogy: Think of parallel capacitors as increasing the

total plate area of a single large capacitor. Since
capacitance is directly proportional to plate area,
connecting capacitors in parallel increases the overall
capacitance.

2. Capacitors in Series

When capacitors are connected in series, the reciprocal

of their individual capacitances add up to give the
reciprocal of the equivalent capacitance, resulting in a
smaller total capacitance.
Characteristics of Series Combination:
* Charge: The charge stored on each capacitor in a
series combination is the same.
* Voltage: The total voltage applied across the series
combination is divided among the individual capacitors.
* Effective Capacitance (Cs): The reciprocal of the total
capacitance is the sum of the reciprocals of the
individual capacitances.

Formula for Series Capacitors:

For n capacitors (C1, C2, C3, ..., Cn) connected in
series, the equivalent capacitance is:
1/Cs = 1/C1 + 1/C2 + 1/C3 + ... + 1/Cn
For two capacitors in series,Cs = (C1 * C2) / (C1 + C2)

Analogy: Think of series capacitors as increasing the

effective distance between the plates of a single large
capacitor. Connecting capacitors in series decreases the
overall capacitance.

3. Mixed Combination

Circuits often involve a combination of series and

parallel capacitor arrangements. To calculate the
equivalent capacitance of such a circuit, you would
typically simplify the circuit step-by-step, combining
series and parallel groups until a single equivalent
capacitance is found.
Energy stored in Capacitor
The process of charging a capacitor involves moving
charge from one plate to the other against the electric
field created by the already accumulated charges. This
requires work to be done. As more charge is moved, the
potential difference (voltage) across the plates
increases, and more work is needed to move
subsequent charges. This work done is what gets stored
as energy in the capacitor.

Formulas for Stored Energy:

The amount of energy (U) stored in a capacitor depends

on its capacitance (C) and the voltage (V) across its
terminals. Here are the three main ways to calculate it,
using standard text for the formulas:

* Using Capacitance (C) and Voltage (V):

This is the most common formula you'll encounter:
U = 1/2 * C * V^2
(This means half times capacitance times voltage
squared).
This formula clearly shows that the stored energy
increases very quickly with voltage; if you double the
voltage, the energy stored becomes four times greater!

* Using Charge (Q) and Capacitance (C):

 U = 1/2 * Q^2 / C
(This means half the charge squared divided by
capacitance).
This formula is useful if you know the amount of
charge stored and the capacitor's capacitance.

* Using Charge (Q) and Voltage (V):

U = 1/2* Q * V
(This means half times charge times voltage).
This relates the stored energy directly to the total
charge and the final voltage.

Units:
* U (Energy) is measured in Joules (J).
* Q (Charge) is measured in Coulombs (C).
* C (Capacitance) is measured in Farads (F).
* V (Voltage) is measured in Volts (V).

Where is this Energy Used?

Capacitors that store energy are used everywhere!

* In camera flashes, they release a quick burst of light.
* Defibrillators use large capacitors to deliver a powerful
electrical shock to the heart.
* In power supplies, they smooth out voltage
fluctuations, providing a steady flow of power.
* They're also found in things like pulsed lasers, radar
systems, and even for memory backup in some devices
during brief power outages.