Resistors

Resistors are vital components in electronic circuits, regulating current flow, managing voltage levels, and safeguarding other components.
By controlling the flow of electricity, resistors ensure circuits operate safely and effectively.

Definition and Role

A resistor, a passive electronic component with two terminals, impedes the flow of current in a circuit. Its resistance, measured in ohms
(Ω), determines how much it restricts the current flow. With a dimensional formula of \( ML^2A^{-2}T^{-3} \), resistance is derived from
mass (M), length (L), area (A), and time (T).

Functions and Applications

1. Current Regulation:

- Control and Limitation: Resistors manage current, preventing excess flow and ensuring components operate within safe limits.

- Current Division: In circuits with multiple resistors, current can be divided among different paths, each with specific resistance.

2. Voltage Management:

- Voltage Division: Used in voltage dividers, resistors reduce input voltage to manageable levels.

- Voltage Setting: They establish desired voltage levels across circuit components.

3. Protection:

- Overcurrent Prevention: By limiting current, resistors protect sensitive components from damage.

- Surge Absorption: Resistors dissipate sudden electrical surges, safeguarding the circuit.

4. Achieving Desired Behaviour:

- Signal Filtering: Used in filters to allow or block specific frequencies.

- Transistor Biasing: Set the operating point for transistors, ensuring proper functionality.

Types of Resistors

1. Fixed Resistors:

- Carbon Composition: Stable resistance value, suitable for general use.

- Metal Film: Provide precise resistance with minimal temperature effects.

- Wire-Wound: Designed for high-power applications, with a metal wire wound around an insulating core.

2. Variable Resistors:

- Potentiometers: Adjustable resistance, commonly used in volume controls.

- Rheostats: Handle higher currents, used for current adjustment in power applications.

3. Special Resistors:

- Thermistors: Resistance varies with temperature, used for temperature sensing.

- Photoresistors: Resistance changes with light intensity, ideal for light-sensitive applications.

Importance in Circuits

Resistors play a crucial role in ensuring electronic circuits function reliably and efficiently. By selecting appropriate resistor values and
types, engineers can fine-tune circuit performance to meet specific requirements, making resistors indispensable in electronic design.
A Resistor contains four bands as shown in the below image:
 Band A in a resistor represents 1st digit.
 Band B in a resistor represents the 2nd digit.
 Band C in a resistor represents a Multiplexer.
 Band D in a resistor represents the % of Tolerance.

The Resistor can be denoted by its Value and name like R1 , R2 .The terminals of the resistor are
represented by each lines which are extending from the squiggle or rectangle. The resistance value, typically
expressed in ohms, is fundamental for circuit analysis and construction.
Different Types of Resistors
There are different types of resistors, which are mainly classified into
 Linear Resistors
 Non-Linear Resistors.

Linear resistors, which include fixed and variable types, play crucial roles in electronic circuits, offering stable
resistance or adjustable values.

Fixed Resistors:

Fixed resistors maintain a constant resistance, vital for circuits requiring stable values. They adhere to Ohm's
law, where voltage (V) is directly proportional to current (I) and resistance (R). Types include: Carbon Film
Resistors Wire Wound
Resistors Metal Film
Resistors

Variable Resistors:

Variable resistors allow resistance adjustment, often through dials or knobs. These are pivotal in
applications needing adjustable resistance, such as volume controls or sensor circuits. Types
comprise:

- Potentiometers

- Rheostat Resistors
- Trimmer Resistors

### Non-Linear Resistors:

Unlike linear resistors, non-linear ones exhibit significant resistance changes with varying
voltage or current. They don't adhere to Ohm's law, and their resistance values fluctuate with
temperature and applied voltage. Used mainly in applications requiring variable resistance, they
include:

- Thermistors (NTC and PTC)

- Varistors

- Photo Resistors

These resistors cater to diverse needs, from stable resistance requirements in fixed circuits to
adjustable resistance in variable applications, ensuring efficient circuit operation across various
electronic systems.

Resistor Color Code

The value of resistance offered by a resistor is marked using a color code called
Resistor Color Code. The resistors we use are very tiny and the printing of the
value of resistance in the resistor is not feasible. Thus, to find the value of the
resistor we use various color bands(mainly four color bands) that help to
determine the value of the resistance. These color bands on the resistor are
called the Resistor Color Codes .
1. Mnemonic of Resistor Color Code: Learning the Resistor Color Coding is
very important and the mnemonic used to find the value of the resistor is:
 The capital letters represent the first letters of the colors and their
positions in the digit values. The representation of the color code as,
 Black, Brown, Red, Orange, Yellow, Green, Blue, Violet, Grey, and
White
Combination of Resistors
Resistors are used in various combinations. There are two methods of arranging
the resistors in different combinations:
 Resistors in Series Combination
 Resistors in Parallel Combination
Equivalent Resistance: The equivalent resistance of combinations of resistors in
series is equal to the sum of their individual resistances in the circuit.
1. Resistors in Series Combination
Two or more resistances are said to be connected in series when they are
connected end to end and the same current flows through each of them in turn.
In this case, the equivalent or the total resistance equals the sum of the
number of individual resistances present in the series combination.
Mathematically, the equivalent resistance of any number of resistances (R1, R2,
R3, R4, R5, ……..) connected in series is given as:
Req = R1 + R2 + R3 + R4 + R5 + ……..
2. Resistors in Parallel Combination
Two or more resistances are said to be connected in parallel connected when
they are connected between two points and each has a different current
direction. The current is branched out and recombined as the branches
intersect at a common point in such circuits.
Mathematically, the equivalent resistance of any number of resistances (R1, R2,
R3, R4, R5, ……..) connected in parallel is given as:
1/Req = 1/R1 + 1/R2 + 1/R3 + 1/R4 + 1/R5 + …..
Power Dissipated in a Resistor

𝑃=𝐼2𝑅=𝑉𝐼=𝑉2P=I2R=VI=V2
The Formula for the power Dissipation in the resistor can be given as

The following equation is derived from Joule’s law and Ohm’s law.
Working Principle of Resistor
Resistor is an passive electronic component which limits the flow of electric
current in an electric circuit. It works on the principle of electrical resistance. It
works mainly on resistance of an electrical circuit. Resistance has a property to
opposes the flow of electric current. Resistance is measured in ohms(Ω).The
more and the higher the resistance value of a resistor, the more it can restricts
the flow of current passing through it.
By using Ohm’s Law: Resistor working principle can be explained using
Ohm’s Law, which states that the current (I) flowing through a conductor is
directly proportional to the voltage (V) across it and it is inversely proportional
to its resistance (R). Mathematically, Ohm’s Law is represented as follows : V =
I*R
Where,
 V stands for, the voltage across the resistor in volts (V).
 I stands for, the current passing through the resistor in amperes(A).
 R stands for, the resistance of the resistor in ohms(Ω).
Calculate the Resistance Value
 We need to consider the specific requirements of your circuit.
 We need to use Ohm’s law (R = V/I) to calculate it based on the
required voltage (V) and current (I).
 We need to use R=V/I is the formula to calculate resistance value.

Applications of Resistor
 Resistors are mainly used in voltage division, as it helps to divide the
voltage to its desired level in applications.
 Resistors are mainly used in limiting the current flow in any electrical component.
 Resistors are used in voltage regulators, sensors and temperature controller.
 Resistors are used in noise reduction process as it regulates the noise path.
Advantages of Resistors
The main advantages of using resistor in a electrical circuit are:
 Resistor helps in precise control of current and voltage in electrical circuit.
 Resistors can also be used as voltage dividers and current limiters in electrical
circuit.
  Resistors are reliable, durable and they have a long operational life which helps in
electrical circuits.
Disadvantages of Resistors
 Resistors are mainly designed for specific resistance values only, finding correct
resistor sometimes may feel difficult.
 Resistors which are having high resistance will oppose large amount of electric
current. so that the large amount of energy is wasted in the form of heat.
Conclusion
In conclusion, Resistors are main and fundamental components in an electrical components.
They can help many electrical circuits to control current, voltage, and resistance with correct
precision and reliability. Resistors has many applications in daily life. These are mainly used in
electrical circuits. There are many different types of resistors. these each type of resistor is used
in different types of circuits according their use. Resistors can help to control the flow of current,
voltage and resistance.
Transistors
A transistor is a semiconductor device used to amplify or switch electrical signals and power, serving as a fundamental component of
modern electronics. It typically has at least three terminals: base, collector, and emitter. A voltage or current applied to one pair of
terminals controls the current through another pair, enabling signal amplification. Transistors are either packaged individually or
embedded in integrated circuits, making them essential in modern electronics.

Parts of a Transistor

- Base: Activates the transistor.

- Collector: Positive lead.

- Emitter: Negative lead.

Transistors operate by allowing current to flow through channels controlled by the voltage or current at the terminals. Most transistors are
made from pure silicon or germanium, though other semiconductor materials are sometimes used. Compared to vacuum tubes, transistors
are smaller and require less power, though vacuum tubes may perform better at very high frequencies or voltages.

Transistors' low cost, flexibility, and reliability have made them ubiquitous, replacing electromechanical devices in many applications. They
can amplify signals or act as electrically controlled switches, making them vital in digital circuits for both high-power and low-power
applications.

Types of Transistors

1. Bipolar Junction Transistor (BJT):

 - Terminals: Base, Collector, Emitter

- A small current at the base controls a larger current between the collector and emitter.

2. Field-Effect Transistor (FET):

- Terminals: Gate, Source, Drain

- A voltage at the gate controls a current between the source and drain.

Applications

Transistors are used as switches in digital circuits, toggling between "on" and "off" states. Important parameters include the current
switched, voltage handled, and switching speed. Ideal transistors aim to minimize leakage currents when off, reduce resistance when on,
and ensure fast transitions between states.

Simplified Operation

In a grounded-emitter transistor circuit, as the base voltage rises, the emitter and collector currents increase exponentially, reducing the
resistance between collector and emitter. When the voltage difference between collector and emitter is near zero, current flows freely, and
the switch is "on" (saturation).

Transistors are categorized by their structure (e.g., MOSFET, BJT, JFET, IGBT), semiconductor material (e.g., silicon, germanium, gallium
arsenide), electrical polarity (NPN, PNP for BJTs; N-channel, P-channel for FETs), performance (power rating, operating frequency), and
physical packaging. They can operate across a wide temperature range and are tailored for specific applications such as switches, general-
purpose use, and high-frequency operations.

Structure

 MOSFET (IGFET)
 BJT (Bipolar Junction Transistor)
 JFET (Junction Field-Effect Transistor)
 IGBT (Insulated-Gate Bipolar Transistor)
 Other Types

Semiconductor Material

 Metalloids: Germanium (first used in 1947) and Silicon (first used in 1954) in various forms (amorphous, polycrystalline,
monocrystalline).
 Compounds: Gallium arsenide (1966) and Silicon carbide (1997).
 Alloy: Silicon-germanium (1989).
 Allotrope of Carbon: Graphene (research ongoing since 2004).

Electrical Polarity

 NPN and PNP for BJTs

 N-channel and P-channel for FETs

Performance

 Maximum Power Rating: Low, medium, high.

 Maximum Operating Frequency: Low, medium, high, radio (RF), microwave frequency. The maximum effective frequency is
denoted by fT (transition frequency).
 Application: Switch, general purpose, audio, high voltage, super-beta, matched pair.
 Physical Packaging: Through-hole metal, through-hole plastic, surface mount, ball grid array, power modules.
 Amplification Factor: hFE, βF (transistor beta), or gm (transconductance).
 Working Temperature:
o Traditional: −55 to 150 °C (−67 to 302 °F).
o Extreme Temperature: Above 150 °C (302 °F) and below −55 °C (−67 °F).

A transistor might be described by a combination of these characteristics, such as a silicon, surface-mount, BJT, NPN, low-
power, high-frequency switch.
The JEDEC part numbering scheme, developed in the 1960s in the U.S., typically starts with "2N" for three-terminal transistors and "3N" for
four-terminal dual-gate field-effect transistors. The prefix is followed by a two-, three-, or four-digit number that doesn't indicate device
properties. For instance, 2N3055 is a silicon NPN power transistor, while 2N1301 is a PNP germanium switching transistor. A letter suffix like
"A" may indicate a newer variant.

In Japan, the JIS semiconductor designation begins with "2S" (e.g., 2SD965), though the "2S" prefix is sometimes omitted on the package.
Suffixes such as R, O, and BL indicate tighter hFE (gain) groupings.

Manufacturers often use proprietary numbering systems. For example, CK722 was a specific manufacturer's code. Prefixes like "MPF" in
MPF102, originally denoting a Motorola FET, are now unreliable indicators of the manufacturer. Sometimes proprietary schemes borrow
from other naming conventions, such as PN2222A, a plastic-cased version of 2N2222A.

Military parts have their own codes, like the British Military CV Naming System. Manufacturers also use "house numbers" for large orders,
reflecting specific purchasing specifications rather than standardized numbers. For example, HP part 1854-0053 is a JEDEC 2N2218
transistor, also known as CV7763.

Ambiguity can arise from multiple naming schemes and the abbreviation of part numbers. Different devices may share the same marking
(e.g., J176), and as through-hole transistors gain surface-mount counterparts, many new part numbers emerge due to varying pinout
arrangements and options for dual or matched devices. Thus, while original devices like 2N3904 are standardized, their newer versions are
not.
Other Types
The BJT and FET are the main types of transistor based on how the circuit can be used, other
than these two there are more types of transistor such as
 MOSFET (Metal-Oxide-Semiconductor Field-Effect Transistor): It uses an
insulated gate to control the flow of electrons.
 JFET (Junction Field-Effect Transistor): Controls current with electric field applied
across a semiconductor material.
 IGBT (Insulated-Gate Bipolar Transistor): Combines features of both MOSFET
and bipolar junction transistor (BJT) which is used in high-power applications.
 Thin-Film Transistor (TFT): It is used in flat-panel displays and sensors.
  HEMT (High Electron Mobility Transistor):It is used for high-speed operation and
low noise performance.
 ITFET (Inverted-T Field-Effect Transistor):It uses inverted-T-shaped gate
structure for improved performance.
 FREDFET (Fast-Reverse Epitaxial Diode Field-Effect Transistor): It is used for
high-speed switching applications with low reverse recovery time.
 Schottky Transistor: It uses Schottky barrier at the base-collector junction to
improve switching speed.
 Tunnel Field-Effect Transistor (TFET):It is used for low-power operation.
 OFET (Organic Field-Effect Transistor):It is used for flexible electronics and
displays.
 Diffusion Transistor: It uses diffused semiconductor junction for amplification.

How do Transistors Work?

As we know BJT consists of three layers or terminals which are Emitter, Base, and Collector. It
is a device where two P-N junctions are there within a BJT.
 One P-N junction exists between the emitter and base region, and the second
junction exists between the collector and base region.
 Transistors are combined to form a logic gate in which it compares multiple input
current and provide output.
Transistors are used in complex switching circuits which comprise all modern telecommunication
systems.
In the operation of BJT, the base-emitter is forward-biased and the base-collector is reversed-
biased.

Characteristics of Transistor
It represents the plot or structure which represents the relation between current and voltage of a
transistor in a specific configuration. The characteristics of a Transistor are:
 Input Characteristics: It gives the information about the change in input current
with varying voltage having constant output voltage.
 Output Characteristics: It is a plot of an output current with output voltage having
constant input voltage.
 Current Transfer Characteristics: This graph shows the relation between output
current and input current by keeping the voltage constant.
Transistor Biasing
It is a process of applying a DC operating voltage condition to the transistor so that the AC input
signal can be amplified correctly by the transistor. It is one of the most used semiconductor
devices that is used for a wide range of applications. To obtain those functionality a transistor
must be supplied with current or voltage. It can be accomplished by various biasing circuits and
techniques.
Types of Transistor Biasing
Well, in this particular context we will see types of transistor biasing and the most common
preferred methods for biasing of transistor are as mentioned below.
 Base Resistor: The base terminal of the transistor is connected with a high value of
the base resistor and the transistor used in the circuit is of NPN type so that the other
end of the resistor will be connected to the positive part of the supply. It makes the
junction base-emitter to be forward biased and the terminal base will be positive
compared to the emitter terminal.
 Collector To Base: In this collector-to-base biasing the circuit consists of a base
resistor which is fed back to the terminal collector. It is different from the method of
base resistor. Note that if the current at the collector tends to increase the voltage at
the load resistor gets increased which results in an increase in the value of the
voltage at the collector-emitter and the current at the base will be reduced.
 Voltage Divider: This type of biasing is widely preferred because it consists of two
resistors. This biasing helps in providing stabilization due to the resistor present at
the emitter and one disadvantage of using this type of biasing is here the signals
tend to get mixed while using this bias in the circuits.
Transistor Operating Conditions
When a small signal is applied between one pair of terminals in a transistor, a signal can be
operated to control a much larger signal at another pair of terminals. In this part, the property of
the transistor is gained due to signal strength in the process of switching and the output
generated can be either voltage or current or electronic signal. If the input increases then the
output also increases. In other words, it is simple to say that output is proportional to input. Due
to this particular activity transistor can act as an amplifier.
The main use of a transistor is that it makes the circuit more controllable and the current flow is
determined by other circuit elements. Depending on the biasing conditions like forward or
reverse, transistors have three major modes of operations cutoff, active, and saturation regions.
 Active Mode: In this mode, the transistor is generally used as current amplifier. In
active mode, two junctions are differently biased which means emitter-base
junction is forward biased whereas collector-base junction is reverse
biased. In this mode, current flows between emitter and collector and the amount of
current flow in proportional to the base current.
 Cutoff Mode: Here both collector base junction and emitter junction are
reverse biased. As both the PN junction are reverse biased, there is almost no
current flow except very small leakage of currents. In BJT mode it is switched OFF and
is essentially an open circuit. This region is mainly used in switching and digital logic
circuits
 Saturation Mode: In this particular mode of operation, both the emitter-base
and collector-base junctions are forward biased. Here current flows freely from
collector to emitter with almost 0 resistance. In this mode, the transistor is fully
switched ON and it is a closed circuit. It is mainly used in switching and digital logic
circuits.
Applications of Transistor
Transistors are fundamental building blocks of modern electronics. They are essentially tiny,
solid-state switches that can amplify or regulate a current or voltage. Here are some of their key
applications:
 Switch: Transistors can function like electronic switches. By applying a small
voltage, a large current flow can be controlled on or off. This capability is crucial for
digital circuits, the foundation of modern computers and many other devices.
 Amplifier: Transistors can take a weak electrical signal and make it much stronger.
This is essential for applications such as hearing aids, amplifiers for musical
instruments, and radio technology.
 Integrated Circuits (ICs): Transistors are miniaturized and embedded in large
numbers onto tiny silicon chips to create complex integrated circuits. These ICs are
the heart of modern electronics, found in everything from smartphones and
computers to cars and medical devices.
 Memory: Transistors are used in various memory devices, such as Random Access
Memory (RAM) and Flash memory, which enable electronic devices to store and
retrieve data.
 Logic Gates: Transistors can be combined to form logic gates, the basic building
blocks of digital circuits. Logic gates perform basic operations like AND, OR, and NOT,
which allows for complex computations within electronic devices.

Capacitor and Capacitance

Capacitor and Capacitance are related to each other as capacitance is

nothing but the ability to store the charge of the capacitor. Capacitors
are essential components in electronic circuits that store electrical
energy in the form of an electric charge. They are widely used in various
applications, including power supplies, filtering circuits, timing circuits,
and coupling circuits. The ability of a capacitor to store electrical energy
is determined by its capacitance, which is a measure of the amount of
charge that can be stored per unit of the voltage applied. Understanding
the fundamentals of capacitors and capacitance is important for anyone
working with electronic circuits or interested in electronics.
Capacitor
A Capacitor is a two terminal electronic device that has the ability to
store electrical energy in the form of electric charge in an electric
field. It is a physical object.

It consists of two conductors generally plates and an insulator (air, mica, paper,
etc.) separated by a distance. The space between the conductors is filled by a
vacuum or with an insulator known as a dielectric. It stores energy by taking
pairs of opposite charges. The dielectric material allows each plate to hold an
equal and opposite charge. It is also called electric condensers. Capacitors
are a simple passive device that is used to store electrical charge and they are
invented by Ewald Georg von Kleist in 1745.
How Does a Capacitor Work?

Capacitor is one of the basic components of the electric circuit, which can store electric
charge in the form of electric potential energy. It consists of two conducting surfaces
such as a plate or sphere, and some dielectric substance(air, glass, plastic, etc.)
between them.
A capacitor is an electronic component that is designed to store electric charge. It
consists of two conductive plates that are separated by a dielectric material, such as air
or a plastic film. When a voltage is applied across the plates, electrons build up on one
plate and are drawn away from the other, causing an electrical charge to accumulate.
The amount of charge that a capacitor can store is determined by its capacitance,
which is measured in farads (F). The capacitance of a capacitor depends on the surface
area of its plates, the distance between them, and the dielectric constant of the
material between them.
Capacitors are used in a variety of electrical and electronic circuits. For example, they
can be used to filter out unwanted noise or voltage spikes, to store energy in power
supplies, or to tune resonant circuits in radios and other electronic devices. They can
also be used in timing circuits, where they are charged and discharged at specific
intervals to create precise timing signals.

RIPPLE CURRENTS
Ripple current is the AC component of an applied source (often a switched-mode power supply) whose frequency
may be constant or varying. Ripple current causes heat to be generated within the capacitor due to the dielectric
losses caused by the changing field strength together with the current flow across the slightly resistive supply
lines or the electrolyte in the capacitor. The equivalent series resistance (ESR) is the amount of internal series
resistance one would add to a perfect capacitor to model this.
Some types of capacitors, primarily tantalum and aluminum electrolytic capacitors, as well as some film
capacitors have a specified rating value for maximum ripple current.

 Tantalum electrolytic capacitors with solid manganese dioxide electrolyte are limited by ripple
current and generally have the highest ESR ratings in the capacitor family. Exceeding their ripple
limits can lead to shorts and burning parts.
 Aluminum electrolytic capacitors, the most common type of electrolytic, suffer a shortening of life
expectancy at higher ripple currents. If ripple current exceeds the rated value of the capacitor, it
tends to result in explosive failure.
 Ceramic capacitors generally have no ripple current limitation[citation needed] and have some of the lowest
ESR ratings.
 Film capacitors have very low ESR ratings but exceeding rated ripple current may cause
degradation failures.
Capacitance instability[edit source]
The capacitance of certain capacitors decreases as the component ages. In ceramic capacitors, this is caused by
degradation of the dielectric. The type of dielectric, ambient operating and storage temperatures are the most
significant aging factors, while the operating voltage usually has a smaller effect, i.e., usual capacitor design is to
minimize voltage coefficient. The aging process may be reversed by heating the component above the Curie
point. Aging is fastest near the beginning of life of the component, and the device stabilizes over time.
[47]
Electrolytic capacitors age as the electrolyte evaporates. In contrast with ceramic capacitors, this occurs
towards the end of life of the component.
Temperature dependence of capacitance is usually expressed in parts per million (ppm) per °C. It can usually be
taken as a broadly linear function but can be noticeably non-linear at the temperature extremes. The temperature
coefficient may be positive or negative, depending mostly on the dielectric material. Some, designated C0G/NP0,
but called NPO, have a somewhat negative coefficient at one temperature, positive at another, and zero in
between. Such components may be specified for temperature-critical circuits. [48]
Capacitors, especially ceramic capacitors, and older designs such as paper capacitors, can absorb sound waves
resulting in a microphonic effect. Vibration moves the plates, causing the capacitance to vary, in turn inducing AC
current. Some dielectrics also generate piezoelectricity. The resulting interference is especially problematic in
audio applications, potentially causing feedback or unintended recording. In the reverse microphonic effect, the
varying electric field between the capacitor plates exerts a physical force, moving them as a speaker. This can
generate audible sound, but drains energy and stresses the dielectric and the electrolyte, if any.

Dielectric absorption[edit source]

Capacitors made with any type of dielectric material show some level of "dielectric absorption" or "soakage". On
discharging a capacitor and disconnecting it, after a short time it may develop a voltage due to hysteresis in the
dielectric. This effect is objectionable in applications such as precision sample and hold circuits or timing circuits.
The level of absorption depends on many factors, from design considerations to charging time, since the
absorption is a time-dependent process. However, the primary factor is the type of dielectric material. Capacitors
such as tantalum electrolytic or polysulfone film exhibit relatively high absorption,
while polystyrene or Teflon allow very small levels of absorption.[50] In some capacitors where dangerous voltages
and energies exist, such as in flashtubes, television sets, microwave ovens and defibrillators, the dielectric
absorption can recharge the capacitor to hazardous voltages after it has been shorted or discharged. Any
capacitor containing over 10 joules of energy is generally considered hazardous, while 50 joules or higher is
potentially lethal. A capacitor may regain anywhere from 0.01 to 20% of its original charge over a period of
several minutes, allowing a seemingly safe capacitor to become surprisingly dangerous. [51][52][53][54][55]
Leakage[edit source]
No material is a perfect insulator, thus all dielectrics allow some small level of current to leak through, which can
be measured with a megohmmeter.[56] Leakage is equivalent to a resistor in parallel with the capacitor. Constant
exposure to factors such as heat, mechanical stress, or humidity can cause the dielectric to breakdown resulting
in excessive leakage, a problem often seen in older vacuum tube circuits, particularly where oiled paper and foil
capacitors were used. In many vacuum tube circuits, interstage coupling capacitors are used to conduct a
varying signal from the plate of one tube to the grid circuit of the next stage. A leaky capacitor can cause the grid
circuit voltage to be raised from its normal bias setting, causing excessive current or signal distortion in the
downstream tube. In power amplifiers this can cause the plates to glow red, or current limiting resistors to
overheat, even fail. Similar considerations apply to component fabricated solid-state (transistor) amplifiers, but,
owing to lower heat production and the use of modern polyester dielectric-barriers, this once-common problem
has become relatively rare.

Lifespan[edit source]
All capacitors have varying lifespans, depending upon their construction, operational conditions, and
environmental conditions. Solid-state ceramic capacitors generally have very long lives under normal use, which
has little dependency on factors such as vibration or ambient temperature, but factors like humidity, mechanical
stress, and fatigue play a primary role in their failure. Failure modes may differ. Some capacitors may experience
a gradual loss of capacitance, increased leakage or an increase in equivalent series resistance (ESR), while
others may fail suddenly or even catastrophically. For example, metal-film capacitors are more prone to damage
from stress and humidity, but will self-heal when a breakdown in the dielectric occurs. The formation of a glow
discharge at the point of failure prevents arcing by vaporizing the metallic film in that spot, neutralizing any short
circuit with minimal loss in capacitance. When enough pinholes accumulate in the film, a total failure occurs in a
metal-film capacitor, generally happening suddenly without warning.

A capacitor consists of two conductors separated by a non-conductive region.[24] The non-conductive region can
either be a vacuum or an electrical insulator material known as a dielectric. Examples of dielectric media are
glass, air, paper, plastic, ceramic, and even a semiconductor depletion region chemically identical to the
conductors. From Coulomb's law a charge on one conductor will exert a force on the charge carriers within the
other conductor, attracting opposite polarity charge and repelling like polarity charges, thus an opposite polarity
charge will be induced on the surface of the other conductor. The conductors thus hold equal and opposite
charges on their facing surfaces,[25] and the dielectric develops an electric field.

Energy Stored in Capacitor

Once a capacitor is connected to the power source, it started to accumulate
electrons on one surface and the opposite charges on the other surface. The
work done by the power source for this is stored in the capacitor in the form of
electrical potential energy and this energy stored in a capacitor is given by the
equation:
U = (1/2)CV2
Where
 U is the energy stored in joules (J),
 C is the capacitance of the capacitor in farads (F), and
 V is the voltage across the capacitor in volts (V).
Derivation of Energy Stored in Capacitor
Consider a capacitor of capacitance C, which is charged to a potential difference V.
The charge Q on the capacitor is given by the equation Q = CV, where C is the
capacitance and V is the potential difference.
The work done in charging the capacitor from an uncharged state (where Q = 0) to a
charged state dQ with potential V is given by the equation:
dW = VdQ
As V = Q/C, the equation can be written as
dW = Q dQ/C
Integrating both sides of the equation,
W = ∫ Q dQ/C
W = (1/2)Q2/C {Q = CV}
W = (1/2)CV2
This work done is stored in the capacitor as the electric potential energy.
Thus, U = (1/2)CV2

Capacitance
The capacity of a capacitor to store charge in it is called its capacitance. It is an
electrical measurement. It is the property of the capacitor.
Capacitance Formula
When two conductor plates are separated by an insulator (dielectric) in an
electric field. The quantity of charge stored is directly proportional to the

Q∝V
voltage applied and the capacitance of the capacitor.

or
Q = CV
where,
 Q is charge stored.
 C is Capacitance of the capacitor.
 V is voltage applied.
Unit of Capacitance
The standard unit OR the SI unit of capacitance is Farad, but 1 farad is a very large unit
of capacitance. So, capacitance is measured in milifarads, microfarads, picofarads,
nanofarads, etc.
As mili, micro, pico, and nano are the standard prefixes representing the following
relations:
 1 millifarad (mF) = 10-3 Farads
 1 microfarad (μF) = 10-6 Farads
 1 nanofarad (nF) = 10-9 Farads
 1 picofarad (pF) = 10-12 Farads
Series and Parallel Combination of Capacitor

 When the capacitors are connected in a series combination i.e one after the
other, the total capacitance of the capacitors is
1/Ctotal = 1/C1 + 1/C2
Ctotal = (C1C2)/(C1+C2)
  When the capacitors are connected in parallel combination i.e connected
side by side

Ctotal = C1+C2
Capacitance of Parallel Plate Capacitor

A parallel plate capacitor is shown in the image added below,

The capacitance of a parallel plate capacitor is directly proportional to the area

(A) of the two parallel plates and inversely proportional to the distance of

C ∝ A/d
separation between the two plates (d)

C = ∈oA/d
or

 ∈o = permittivity of free space = 8.854 × 10 -12

where

Capacitance of Spherical Capacitor

A Spherical Capacitor is shown in the image added below,

Spherical Capacitor is made up of two hollow concentric conducting shells of

radii R1 and R2 with a dielectric substance between them. These shells have
equal and opposite charge Q. Capacitance of this capacitor is given by
where
 εo = permittivity of free space = 8.854 × 10 -12
Factors affecting Capacitance

There are some factors that can affect the capacitance of capacitors, which are,
 Dielectric
 Distance Between Surfaces
 Area of the Surfaces
Now let’s learn about each in detail.
Dielectric
The dielectric material between both surfaces can affect the capacitance of capacitors
drastically. The capacitance of any capacitor is proportional to the permittivity of the
dielectric i.e., the higher the permittivity of the dielectric higher the capacitance of that
capacitor.
The dielectric constant and permittivity of various dielectrics materials are given as
follows:

Dielectric Permittivity of Dielectric

Vacuum 1
Air 1.0006
Teflon 2.1 – 2.3
Glass 4.5 – 10
Water 80.4
Ethanol 24.3
Glycerol 42.5
Silicon Dioxide 3.7 – 4.9

Distance Between Surfaces

Distance between the surface of the capacitor is inversely proportional to its
capacitance i.e., a higher distance between the surfaces implies a lesser capacitance of
the capacitor. If the capacitance of a capacitor is C and the distance between the

C ∝ 1/d
surface is d then,

Area of the Surfaces

The area of the surface building up the capacitor can affect the capacitance of that
capacitor in a direct proportion i.e., a higher surface area capacitor produces a higher
capacitance capacitor. If C is the capacitance and A is the surface area of one side of

C∝A
the capacitor, then.

Uses of a Capacitor

Capacitors are important components in electronic circuits. They can store electrical
energy and release it as needed, which makes them useful for powering devices and
stabilizing voltage. Capacitors can also filter out unwanted signals, create timing
circuits, transfer signals between circuits, and isolate circuits from each other to
prevent interference. They are used in various fields, including telecommunications,
automotive, aerospace, and consumer electronics.