Fundamental of electro system note for computer engineering students: unite 5: level class: 9

Definition of a Cell

A cell is the smallest part of a battery that produces electricity. It has two main parts called electrodes (an anode and a cathode) and something in between them called an electrolyte. These parts work together to turn chemical energy into electrical energy. A single cell can power small devices, like a remote control or a clock.

The primary function of a cell is to convert chemical energy into electrical energy. Think of it as the foundation of a battery, akin to a brick in a wall.

Definition of a Battery

A battery is a group of cells connected together. For example, a single AA battery is one cell, but the battery in your laptop has many cells working together. Batteries can provide more power or last longer by connecting these cells in different ways.

How Are Cells and Batteries Related?

A battery is simply a collection of cells. If you think of a cell as one brick, a battery is like a wall made from those bricks. Whether you use a single cell or a group of them depends on how much energy you need.

Types of Cells and Batteries

1. Primary Batteries.

• Primary batteries, also known as non-rechargeable batteries, are designed for one-time use. Once their energy is depleted, they cannot be recharged or reused. These batteries are typically used in devices that require low power and are not expected to be used frequently.
• The energy stored in primary cells is chemically released in a one-way process, making them ideal for disposal.
• Examples of primary batteries are Alkaline Batteries, Zinc-Carbon Batteries

2. Secondary Batteries

• Secondary batteries, also known as rechargeable batteries, are designed to be used multiple times. They can be recharged and discharged many times before their capacity starts to degrade.
• Secondary batteries are typically more expensive upfront compared to primary batteries but offer long-term cost savings due to their ability to be reused.

Combination of cells:       

Cell can be combined in series and parallel combinations

1. Series Connection of Cells:

• In a series connection, the positive terminal of one cell is connected to the negative terminal of the next cell.
• The total voltage is the sum of the voltages of all the connected cells.
  V_total=V₁+V₂+V₃+⋯+ V_n
• The current remains the same throughout the circuit.

2. Parallel Connection of Cells:

• In a parallel connection, all the positive terminals of the cells are connected together, and all the negative terminals are connected together.
• The total voltage remains the same as the voltage of one cell.
  V_total = V_cell
• The total current is the sum of the currents of all the cells.
  I_total =  I₁+I₂+I₃+⋯+I_n

What is a Capacitor?

• A capacitor is an electronic component designed to store and release electrical energy in a circuit. It consists of two conductive plates (electrodes) separated by an insulating material called a dielectric.
• When connected to a power source, a capacitor accumulates electric charges on its plates, creating an electric field. Electronic circuits widely use capacitors for energy storage, filtering, and signal coupling.

What is Capacitance?

• Capacitance is the measure of a capacitor’s ability to store electric charge. It indicates how much electric charge a capacitor can hold for a given voltage applied across its terminals. Capacitance depends on:
• The surface area of the plates (larger area = higher capacitance),
• The distance between the plates (smaller distance = higher capacitance),
• The type of dielectric material used (materials with higher permittivity increase capacitance).
• Mathematically, capacitance is defined as:

C=Q/V

Where:

• C is the capacitance,
• Q is the charge stored on the plates (in coulombs),
• V is the voltage across the capacitor (in volts).

Unit of Capacitance

• The unit of capacitance is the farad (F), named after the scientist Michael Faraday. A 1-farad capacitor can store 1 coulomb of electric charge when a voltage of 1 volt is applied across its terminals.

Commonly Used Subunits of Farad:

• Microfarad (µF): 1 μF=10−6 F
• Nanofarad (nF): 1 nF=10−9 F
• Picofarad (pF): 1 pF=10−12 F

Factors affecting capacitance

• Capacitances are mainly affected by three main factors, and these are Area of plate, distance between plate and dielectric material use between the plates.

• Area of the Plates: The larger the surface area of the plates, the higher the capacitance. This is because a larger area can store more charge.
• Distance between Plates: The closer the plates are to each other, the higher the capacitance. If the plates are farther apart, the capacitance decreases.
• Dielectric Material: The material between the plates affects the capacitance. A dielectric material (like air, paper, or plastic) helps to increase capacitance. Materials with higher permittivity (like ceramic) can increase the capacitance compared to materials with lower permittivity.
•  
• Voltage across Plates: While the voltage itself doesn’t affect capacitance directly, the amount of charge stored is related to the voltage. A higher voltage can store more charge but doesn’t change the capacitance value.

Series Connection of Capacitance

• In a series connection of capacitors, the capacitors are connected end-to-end such that the same charge ($Q$) flows through each capacitor, but the voltage across each capacitor can differ.
• The total or equivalent capacitance in a series connection is always less than the smallest individual capacitor in the series.

The series connection of the three capacitances is shown in the below diagram.

            Series connection of capacitor

• Let’s consider the capacitance of the capacitors as C₁, C₂, C₃…….C_n, and the equivalent capacitance of the series combination as C. The voltage drops across capacitors are V₁, V₂, V₃…….V_n.
• The total voltage across the series connection is the sum of the voltages across each capacitor:
•  The total voltage across the series connection is the sum of the voltages across each capacitor:           

                                            V_total=V₁+V₂+⋯+V_{n  …………………………(1)}

Now, if Q coulomb be the charge transferred from the source through these capacitors, then,

Now, equation (i) can be written as,

Parallel Connection of Capacitors

• In a parallel connection of capacitors, capacitors are connected such that their positive terminals are connected to a common point, and their negative terminals are also connected to another common point. 
• This means the potential difference across each capacitor is the same, but the total charge is the sum of the individual charges on each capacitor.

• This means the potential difference across each capacitor is the same, but the total charge is the sum of the individual charges on each capacitor.

• The charge Q stored on a capacitor is given by the formula:

                                Q=C⋅V…………………..(1)

• The total charge stored in the parallel combination is the sum of the charges on each capacitor:

  Q_total=Q₁+Q₂+Q₃+⋯+Q_n

Thus, the total charge is:

                   _{CV=VC1+VC2+VC3+⋯+VCn}

              C_TOTALV=V⋅(C1+C2+C3+⋯+Cn)

             C_TOTAL=⋅(C1+C2+C3+⋯+Cn)

The total capacitance for n capacitors connected in parallel is the sum of their individual capacitances:

          C_TOTAL=⋅(C1+C2+C3+⋯+Cn)

This is the formula for capacitors in parallel.

 Compile by :Basant kumar yadav.