February 3, 2026

Explore Our Topics!

Check out the extensive list of topics we discuss: 

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  2. Communication Protocols:
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    - Intrinsic and Extrinsic Semiconductors
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    - Understanding Capacitor and Capacitance
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    Half Adder using Testbench code
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    Half Adder using Testbench code
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  20. Projects on esim:
    Step-by-Step guide on how to Design and Implement a Full Adder using CMOS and sky130nm PDK
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    Simplifying Boolean Equations with Karnaugh Maps - Part:1 Grouping Rules.
    Simplifying Boolean Equation with Karnaugh Maps.

February 2, 2026

Understanding Capacitors and Capacitance — How Electrical Energy Is Stored

 In electronic circuits, energy is not only consumed — it can also be temporarily stored and released when needed. One of the most important components that makes this possible is the capacitor.

In this blog, we’ll understand what a capacitor is, how it works, how it stores energy, and what capacitance really means.




⚙️ What is a Capacitor?

A capacitor is an electronic component that stores electrical energy in the form of an electric field.


🧩 Structure — How It’s Made

A basic capacitor consists of three parts:

  1. Two Conducting Plates – usually made of metal like aluminum or copper.

  2. Dielectric Material – an insulating layer placed between the plates (air, paper, plastic, ceramic, or mica).

  3. Leads / Terminals – used to connect the capacitor into a circuit.

So physically, a capacitor looks like two metal plates separated by a thin insulating film.

The dielectric does not conduct electricity — it helps store charge by preventing electrons from jumping directly from one plate to the other.


⚡ How Does a Capacitor Work?

Before applying voltage:

  • Both plates are electrically neutral, meaning they have an equal number of positive and negative charges.

After connecting the capacitor to a battery:

  1. The negative terminal of the battery pushes electrons toward the bottom plate of the capacitor through the connecting wire.
    → This bottom plate starts accumulating extra electrons and becomes negatively charged.

  2. As electrons pile up on the bottom plate, they repel electrons from the top plate (because like charges repel).

  3. These repelled electrons from the top plate move through the external circuit toward the positive terminal of the battery, which is electron-deficient and attracts them.

  4. The top plate, having lost electrons, becomes positively charged.

Meanwhile, the dielectric between the plates prevents direct electron flow — it only allows an electric field to form.

As charge separation builds up, a potential difference (voltage) develops across the plates.
This continues until the voltage across the capacitor equals the battery voltage — at that point, charging stops.

The electric field created between the plates stores the electrical energy.

The electric field strength is given by:

E = V / d

where:

  • V = voltage across the plates

  • d = distance between the plates


🔋 Energy Storage in a Capacitor

The capacitor now holds energy in the electric field between its plates.

If the battery is disconnected, the charges remain stored — the capacitor stays charged.

It releases this stored energy only when a conductive path (like a resistor or load) is connected between its plates.
Electrons then flow from the negatively charged plate to the positively charged plate through the external circuit, producing current until both plates become neutral again.

This process is called discharging the capacitor.


🧮 What is Capacitance?

Capacitance is the ability of a capacitor to store electric charge per unit voltage.

In simple terms, it tells how much charge a capacitor can store for a given applied voltage.

Mathematically:

C = Q / V

where:

  • C = capacitance (Farads, F)

  • Q = charge stored (Coulombs)

  • V = voltage across the capacitor (Volts)

A higher capacitance means greater charge storage capability.


⚡ Current–Voltage Relationship in a Capacitor

The relationship between current and voltage for a capacitor is:

I = C (dV/dt)

This means:

  • If voltage changes rapidly, current is large.

  • If voltage is constant, current is zero.

So a capacitor allows current to flow only when voltage is changing.
A capacitor opposes sudden changes in voltage.


🧠 Factors Affecting Capacitance

  1. Area of Plates (A): Larger area → more charge → higher capacitance

  2. Distance Between Plates (d): Greater distance → lower capacitance

  3. Dielectric Constant (ε): Better dielectric → higher capacitance

For a parallel plate capacitor:

C = ε (A / d)

From this:

  • Bigger plates → higher capacitance

  • Closer plates → higher capacitance

  • Better dielectric → higher capacitance


🔥 Energy Stored in a Capacitor

The energy stored in a capacitor is given by:

E = (1/2) C V²


🔚 Conclusion

A capacitor is a fundamental electronic component that stores electrical energy in the form of an electric field. By separating charge across two plates using a dielectric, it plays a crucial role in energy storage, voltage stabilization, filtering, timing circuits, and signal coupling.

Capacitance defines how effectively a capacitor can store charge, and it depends on the physical structure and dielectric material used. Capacitors respond to changes in voltage rather than steady values, which makes them essential in both analog and digital electronics.

Understanding capacitors and capacitance lays a strong foundation for learning RC circuits, filters, power supplies, and advanced analog electronic systems.

Understanding Resistivity: Why Materials Oppose Electric Current

In the previous blog, we understood how resistance controls current in a circuit.

Now let’s go one level deeper and explore resistivity — the fundamental material property that decides why different materials behave differently when current flows. 



⚙️ What is Resistivity?

Resistivity, or specific resistance, is a property of a material that tells how strongly it opposes the flow of electric current.
It is an intrinsic property, meaning it depends only on the material — not on its shape, size, or dimensions.

In simple terms:
Resistivity is like the “resistance nature” of a material — how much that material inherently resists current flow.


🧩 Symbol and Unit

Resistivity is represented by the Greek letter ρ (rho).
Its SI unit is ohm-meter (Ω·m).


🧮 Formula for Resistivity

From the formula for resistance:


We can rearrange it as:


Where:

  • R = Resistance (Ω)
  • L = Length (m)
  • A = Cross-sectional area (m²)
  • ρ = Resistivity (Ω·m)

🔬 Understanding It Conceptually

Let’s say you have two wires made of different materials — copper and nichrome — but both have the same length and thickness.

If you apply the same voltage to both, you’ll find that the current through copper is much higher.
Why? Because copper has a lower resistivity — it allows electrons to move more freely.

Nichrome, on the other hand, has a higher resistivity, so it naturally resists current flow more.

So:

  • Low resistivity → good conductor (like copper, silver, aluminum)
  • High resistivity → poor conductor or insulator (like rubber, glass, or plastic)

🧠 Typical Values of Resistivity

Material

Type

Resistivity (Ω·m)

Silver

Conductor

1.6×10⁻⁸

Copper

Conductor

1.7×10⁻⁸

Aluminum

Conductor

2.8×10⁻⁸

Nichrome

Resistive Alloy

1.1×10⁻⁶

Silicon

Semiconductor

6.4×10²

Glass

Insulator

10¹⁰ – 10¹⁴

This shows how resistivity increases drastically from conductors to insulators.


🌡️ Temperature Dependence of Resistivity

Resistivity is also affected by temperature, and it behaves differently for different types of materials:

  • Conductors: Resistivity increases with temperature.
    As temperature rises, atoms vibrate more, making it harder for electrons to move.

Formula:


where is the temperature coefficient of resistivity.

  • Semiconductors & Insulators: Resistivity decreases with temperature.
    Higher temperature gives more energy to electrons, letting them move more freely.

💡 Simple Analogy

If you imagine current as water flowing through a pipe —
then resistance depends on the length and width of the pipe,
but resistivity depends on what the pipe is made of.

A copper pipe (low resistivity) lets current flow easily,
while a rubber pipe (high resistivity) almost blocks it completely.


⚡ Inside the Resistor: The Electron Story

Have you ever wondered what’s really happening inside a resistor when current flows through it?
Let’s dive into the microscopic world of electrons to understand the real story behind resistance.


🔹 The Journey of Electrons

Electric current is nothing but the movement of electrons through a conductor — usually a metal wire.
Metals like copper or aluminum have free electrons that can easily move from one atom to another.

Now, when you connect a battery to a resistor, here’s what happens step by step:

  • The battery creates an electric field inside the wire.
  • This field pushes the free electrons, giving them a tiny drift — they start moving toward the positive terminal.
  • As these electrons move through the resistive material (like carbon or metal film), they collide with atoms of that material.
  • Each collision causes the electron to lose a small amount of energy, which gets converted into heat.

This process happens billions of times per second inside the resistor!

So, inside a resistor —
electrons are constantly being accelerated by the electric field and then losing energy due to collisions, and that continuous loss of energy is what we call resistance.


⚙️ What’s Happening Physically

If you could zoom in and watch the inside of a resistor at the atomic level, you’d see something fascinating:

  • A sea of free electrons drifting through a fixed lattice of atoms.
  • As electrons move, they bump into these atoms, disturbing them slightly.
  • Each collision converts part of the electrical energy into heat, warming up the resistor.
  • The result — a steady current still flows, but reduced in magnitude compared to what it would be in a perfect conductor.

In essence, resistance is simply the measure of how much these collisions hinder electron flow.


💡 In Simple Words

Think of it like a crowded hallway:

  • The electrons are like people trying to walk through it.
  • The hallway (resistor) is full of obstacles — the atoms.
  • Every time they bump into someone, they lose a bit of speed (energy).

They still move forward, but more slowly — that’s resistance!


🔚 Wrapping Up

A resistor may look tiny, but inside it, an entire world of motion and collisions exists.
Each time current passes through, countless electrons dance their way through a forest of atoms — turning electrical energy into heat and giving us the control we need in circuits.

That’s the real story inside every resistor you see on a circuit board.


🌡️ NTC and PTC Resistors — The Temperature-Sensitive Resistors

Both NTC and PTC are types of thermistors, which are special resistors whose resistance changes significantly with temperature.
The word “thermistor” itself comes from Thermal + Resistor.

Unlike ordinary resistors (whose resistance slightly increases with temperature), thermistors are designed to respond strongly to temperature changes — they’re used as temperature sensors, protectors, and controllers in many circuits.

🔥 Why Does It Get Hot?

Because every collision turns a little bit of the electrons’ kinetic energy into thermal energy.
That’s why resistors warm up when current flows through them — the electrical energy is being converted into heat energy.

This is also how electric heaters or toasters work — they use high-resistance wires (like nichrome) to deliberately produce heat when current flows.


⚙️ Two Main Types

  • NTC (Negative Temperature Coefficient) Resistor → Resistance decreases as temperature increases.
  • PTC (Positive Temperature Coefficient) Resistor → Resistance increases as temperature increases.

Let’s explore both — and then peek inside what’s actually going on at the atomic level.


🧊 NTC Resistor: Negative Temperature Coefficient

When temperature goes up, resistance goes down.

🔍 What’s Happening Inside

NTC thermistors are usually made from semiconducting materials — typically metal oxides like manganese oxide (MnO), nickel oxide (NiO), or cobalt oxide (CoO).

Here’s how it works inside:

  • At low temperatures, only a few electrons in the material have enough energy to jump into the conduction band → limited current flow → high resistance.
  • As temperature rises, atoms vibrate more and give energy to bound electrons.
  • More electrons get freed into the conduction band → more charge carriers become available.
  • More charge carriers = more current flow = lower resistance.

So, the drop in resistance is caused by the increase in the number of free electrons as temperature increases.


💡 Real-life Examples

  • Used in temperature sensors (like in digital thermometers).
  • Used in startup current limiters in power supplies — when cold, high resistance limits current; as it heats, resistance drops, allowing full current.

🔥 PTC Resistor: Positive Temperature Coefficient

When temperature goes up, resistance goes up.

🔍 What’s Happening Inside

PTC thermistors can be made in two main ways — metal alloy type or semiconducting type (like doped barium titanate, BaTiO₃).

Let’s take the semiconductor-based PTC as the main example:

  • At normal temperatures, electrons can move easily, so resistance is relatively low.
  • As temperature increases, the crystal structure of the material changes slightly — it undergoes a phase transition.
  • This transition reduces the mobility of charge carriers and may even trap some of them, drastically increasing resistance.

So, above a certain critical temperature, the material suddenly becomes much more resistive — it’s like a built-in switch that limits current flow.


💡 Real-life Examples

  • Used in self-regulating heaters — when they get hot, resistance increases, limiting the current automatically.
  • Used as overcurrent protectors or resettable fuses — they cut off current when overheated and return to normal when cooled.

⚡ Internal Comparison: NTC vs PTC



🧠 Visual Way to Think About It

Imagine NTC as a crowd of sleepy people who wake up as it gets warmer — more people start moving (electrons conducting), so current flows easily → resistance drops.

Now, imagine PTC as a traffic jam that happens when too many people (electrons) move too fast — the system gets disordered, paths get blocked, and current flow becomes difficult → resistance increases.


🧩 Summary

  • NTC → Heat gives more energy to electrons → easier current flow → resistance decreases.
  • PTC → Heat disrupts structure or traps electrons → harder current flow → resistance increases.
  • Both are thermistors, used where circuits must respond automatically to temperature changes.

🔚 Conclusion — Understanding Resistivity

Resistivity is the root cause behind how materials conduct or resist electric current. While resistance depends on the size and shape of a conductor, resistivity depends purely on the nature of the material itself.

At the microscopic level, resistivity arises from how electrons move through a material and how frequently they collide with atoms in the lattice. Materials with low resistivity allow electrons to flow freely and act as good conductors, while materials with high resistivity strongly oppose current flow.

Temperature further influences this behavior — metals become more resistive when heated, whereas semiconductors become more conductive. Special components like NTC and PTC thermistors take advantage of this property to sense temperature and protect circuits automatically.

Understanding resistivity connects material physics with circuit behavior, forming a strong foundation for advanced topics in electronics, semiconductors, and analog circuit design.

Understanding Resistors: How Resistance Controls Current in Electronic Circuits

Have you ever wondered what prevents the flow of electric current from becoming uncontrollable in circuits?

The answer lies in one of the simplest yet most powerful components in electronics — the resistor.

Let’s explore what resistors are, how they work, and why they are absolutely essential in every electronic device you use.




🧩 What is a Resistor?

A resistor is basically an electronic component that opposes the flow of electric current in a circuit.

Think of it as something that restricts how freely electrons can move through a wire.
This resistance causes a voltage drop, and as a result, electrical energy gets converted into heat.
Without it, your LEDs would burn out, your transistors would fry, and your circuits would go unstable.

When you apply a voltage across a resistor, it doesn’t let all the electrons pass easily — it provides some resistance to their motion.

So, a resistor’s main job is to control current and set voltage levels in a circuit.


⚙️ What is Resistance?

The property of a material that opposes the flow of electric current is called resistance.

It’s denoted by the symbol R and measured in ohms (Ω).
For instance:

  • Metals like copper and silver have low resistance (that’s why we use them for wires).
  • Materials like carbon or nichrome have higher resistance, so we use them to make resistors.
  • R = Resistance (in ohms, Ω)
  • ρ (rho) = Resistivity of the material (Ω·m)
  • L = Length of the conductor (m)
  • A = Cross-sectional area of the conductor (m²)
  • The longer the wire → greater the resistance.
  • The thicker the wire → smaller the resistance.

Every material naturally offers some resistance.

The amount of resistance depends on a few factors:


Where:

So,

Different materials have different resistivities — that’s why choosing the right material matters.


⚡ Relationship Between Voltage, Current, and Resistance — Ohm’s Law

The fundamental law that defines how resistors behave is Ohm’s Law:


Where:

  • V = Voltage across the resistor (in volts)
  • I = Current through the resistor (in amperes)
  • R = Resistance (in ohms)
That’s how resistors help control current flow in a circuit.

This means if you increase the resistance while keeping the voltage same, the current decreases — and vice versa.


🏭 How Resistors Are Made

Resistors come in many forms, but the most common ones are carbon film and metal film resistors.

Here’s a simple idea of how they’re made:

  1. A ceramic rod acts as the base.
  1. A thin film of resistive material (carbon, metal, or metal oxide) is deposited on it.
  1. The thickness and pattern of that film determine the resistance value.
  1. Metal caps are attached at both ends for electrical connection.
  1. The whole thing is coated with insulating paint, often with color bands that indicate its resistance value.

Those color stripes on resistors aren’t random — they’re part of a color code system used to identify their resistance in ohms.


💡 Uses of Resistors

Resistors are used in almost every electronic circuit. Some important uses include:

  • Current Limiting: To prevent excess current from damaging LEDs or ICs.
  • Voltage Division: In voltage divider circuits to get desired voltage levels.
  • Biasing of Transistors: To control base current and set the operating point.
  • Heat Generation: In electric heaters or toasters where resistors convert electrical energy into heat.
  • Pull-up / Pull-down Resistors: To define logic levels in digital circuits.

In short — resistors bring control and stability to electrical and electronic systems.


🚫 What Happens If There Were No Resistors?

Imagine connecting an LED directly to a 9V battery without a resistor.

The LED would glow brightly — but only for a fraction of a second before burning out!

  • Components would overheat and get damaged.
  • Circuit currents would be uncontrolled.
  • Voltage levels would fluctuate, making digital logic unreliable.

That’s because without a resistor, there’s nothing to limit the current, and components receive more current than they can handle.

Without resistors:

So yes, resistors are small but vital for circuit protection and performance.


🧮 Types of Resistors

Resistors come in different types depending on how they’re built and used:

1. Fixed Resistors

Have a constant resistance value.

  • Carbon Composition Resistors – made from a carbon and ceramic mixture.
  • Carbon Film / Metal Film Resistors – more accurate and stable.
  • Wire-wound Resistors – used for high-power applications.
Used in volume controls, dimmers, or tuning circuits.
  • NTC (Negative Temperature Coefficient) – resistance decreases with temperature.
  • PTC (Positive Temperature Coefficient) – resistance increases with temperature.
Used in automatic night lamps and light sensors.

2. Variable Resistors (Potentiometers)

Resistance can be adjusted manually.

3. Thermistors (Temperature-dependent)

4. Photoresistors (LDRs)

Light-dependent resistors — resistance decreases when light intensity increases.

Understanding Electron Shells, Subshells, and Energy Ordering

A Simple Explanation for Electronics and Semiconductor Students


🌍Introduction

Atoms are the foundation of all electronic materials. The way electrons are arranged around the nucleus determines the electrical, optical, and thermal properties of materials. Concepts such as conductors, semiconductors, and insulators are deeply rooted in atomic structure.

In this chapter, we will clearly understand:

  • Electron shells (energy levels)

  • Subshells and orbitals

  • Electron capacity rules

  • Energy ordering of electrons

  • Octet rule and stability

All concepts are explained in simple words, while maintaining scientific correctness.


🔵 Electron Shells (Energy Levels)

In atomic structure, electron shells (also called energy levels) are regions around the nucleus where electrons are likely to be found. Each shell corresponds to a fixed energy value, meaning electrons in that shell have a specific quantized energy.

⚠️ Important clarification:
Electrons do not move in fixed circular paths. Instead, they exist in probability regions called orbitals, which are grouped into shells.

Key Points:

  • Shells are denoted as K, L, M, N…

  • They are also represented using principal quantum numbers:
    n = 1, 2, 3, 4…

  • The shell closest to the nucleus has the lowest energy

  • Outer shells have higher energy because electrons are farther from the nucleus

Why do inner shells have lower energy?

  • The nucleus is positively charged

  • Inner electrons experience stronger electrostatic attraction

  • Outer electrons experience less pull → higher energy

👉 Think of it like climbing floors in a building:
The ground floor (K shell) has the lowest energy, and higher floors represent higher energy levels.


🔢 Maximum Electrons in a Shell – The 2n² Rule

The maximum number of electrons that can occupy a shell is given by:

Maximum electrons in a shell = 2n²

Where n is the shell number.

Calculation Table

Electron Capacity Sequence

  • K → 2

  • L → 8

  • M → 18

  • N → 32

This explains why different elements have different chemical and electrical properties.


🧩 Why Subshells Are Needed

Although the 2n² rule gives the maximum capacity, electrons do not simply fill shells completely one by one.

Each shell is divided into subshells, which represent different electron energy states and shapes.


🔹 What Are Subshells?

Subshells are smaller divisions within a shell that define:

  • Electron shape

  • Electron energy

  • Electron orientation

They are denoted by letters:

  • s

  • p

  • d

  • f

Example:

  • M shell (n = 3) → 3s, 3p, 3d


🔬 Subshells, Orbitals, and Electron Capacity

Each subshell contains orbitals, and:

  • Each orbital can hold 2 electrons

  • Electrons have opposite spins

The number of orbitals in a subshell is given by:

Number of orbitals = 2ℓ + 1

Where ℓ (angular momentum quantum number) defines the subshell type.

Subshell Details Table


🔗 Relationship Between Shells and Subshells

This structure naturally explains the 2n² rule.


⚡ Energy Ordering of Subshells (Aufbau Principle)

Electrons fill orbitals in order of increasing energy, not simply by shell number.

Energy Filling Order:

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s

Why does 4s fill before 3d?

Although 3d belongs to the third shell:

  • The 4s subshell is lower in energy

  • Therefore, electrons occupy 4s first

  • 3d fills only after 4s is filled

This is crucial for understanding transition elements and semiconductor behavior.


🧪 Octet Rule and Atomic Stability

Atoms tend to achieve a stable electronic configuration.
The most stable condition is when the valence shell has 8 electrons, known as the Octet Rule.

Behavior Based on Valence Electrons:

  • 1–3 electrons (Na, Mg, Al) → lose electrons

  • 5–7 electrons (O, F, Cl) → gain electrons

  • 4 electrons (C, Si) → share electrons (covalent bonding)

This explains:

  • Ionic bonding

  • Covalent bonding

  • Chemical reactivity


🔍 Why Is the Octet Rule Stable?

1️⃣ Subshell Explanation

  • Outer shells fill as s → p

  • Second shell has:

    • 2s → 2 electrons

    • 2p → 6 electrons

  • Total = 8 electrons → stable

2️⃣ Noble Gases Proof

  • Neon, Argon, Krypton have full outer shells

  • They are chemically inert

  • Confirms octet stability

3️⃣ Why Not 18 in the 3rd Shell?

  • 3rd shell can hold 18 electrons

  • But 3d fills after 4s

  • Stability depends mainly on 3s + 3p = 8

  • Hence, atoms achieve stability before 3d filling

⚠️ Note:
The octet rule mainly applies to main-group elements and has exceptions, especially for transition metals.


✅ Conclusion

Understanding shells, subshells, and electron energy ordering is fundamental for:

  • Semiconductor physics

  • Band theory

  • Electronic materials

  • Device behavior

This knowledge forms the base of electronics and VLSI engineering.

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