**Introduction to cell
**A cell is a single electrical energy source which uses chemical reactions to produce a current. A cell can be classified as a reserve, wet or dry type according on the types of electrolytes utilized. Moltan salt type is also present in the cell. A cell is typically small and light because it just comprises one unit. It produces power for a shorter amount of time. It is often employed for simpler, lower-energy operations. Clocks, lamps, and other devices use it. It often cost less.

**Battery
**A battery is an electrochemical device consisting of one or more electrical cells that can storage energy in the form of chemical energy.

**Typically, it is made up of many cells. A battery is classified as either a main battery or a secondary battery, depending on whether it can be recharged. It has many cells, which increases its size and makes it bulkier. Power can be provided via a battery for longer periods. The majority of heavy-duty operations require a battery. It is utilized in inverter, vechicles, etc. batteries are substantially more expensive.**

The symbolic representation of cell and battery

**Types of Cell/Battery**

**Primary Cell/Primary Battery
**The batteries that are designed for a single usage and are not rechargeable are referred to as primary batteries. The domestic battery used to power clocks, TV remotes, and other gadgets is known as a dry cell and is an illustration of a primary battery. The anode and cathode of these cells, respectively are carbon rods and zinc containers.

**Secondary Cell/Secondary Battery
**Secondary batteries are batteries designed to be recharged and used repeatedly. They can be recharged by passing current through the electrodes in the reverse way, from the negative terminal to the Positive terminal, after usage, which is why they are also known as rechargeable batteries.

A rechargeable battery is also utilized with an inverter, which stores energy to power our home appliances. In comparison to the primary battery, the secondary is more costly, bulkier, heavier and requires more care.

**Combination of cell
**When electrical devices are connected in a series one after another, it is called a combination of cells in a series, whereas in a combination of cells in a parallel circuit, the current makes its way through two or more paths.

**Series combination
**A set of batteries are said to be connected in series when the positive terminal of one cell is connected to negative terminal of the succeeding cell.

**Advantage
**The design of a combination of cells in a series is simple and easily understandable.

**Quick overheating does not occur.**

**Its higher output voltage assists in the addition of more power appliances.**

**The current that is carried throughout the circuit remains the same.**

**Disadvantage
**An increase in the total number of components increases the circuit resistance.

**The occurrence of a fault at one point in the circuit will break the whole circuit.**

**Parallel combination
**A set of batteries are said to be connected in parallel when the positive terminals of all batteries are connected at one point and similarly, negative terminals of these cells are connected at another point.

**Circuit having parallel connection of cell shows following characteristics:**

**The emf of the battery is same as that of a single cell.**

**The current in the external circuits divided equally among the cells.**

**The reciprocal of the total internal resistance is the sum of the reciprocal of the individual internal resistances.**

**Advantage
**As the voltage is the same across every component in a combination of cells in a parallel circuit, it results in better efficiency.

**Connections or disconnections of new components are hassle-free in a combination of cells in a parallel circuit without adversely impacting other components’ working.**

**Different between cell and Battery**

CELL |
BATTERY |

A single unit device known as a cell transforms chemical energy into electric energy. | Typically, a battery is made up of many cells. |

A cell can be classified as a reserve, wet, or dry type according on the types of electrolytes utilized. | A battery is classified as either a main battery or a secondary battery, depending on whether it can be recharged. |

Because it just comprises one unit, a cell is typically small and light. | A battery typically has many cells, which increase its size and makes it bulkier. |

For a shorter amount of time, a cell produces power. | Power can be provided via a battery for longer periods. |

A cell is often employed for simpler, lower-energy operations. | The majority of heavy-duty operation requires a battery. |

Cells often cost less. | Batteries are substantially more expensive. |

**Capacitor, capacitance and its units:
** A capacitor is an electronic component that stores and releases electrical energy in a circuit. It consists of two conductive plates separated by an insulating material called a dielectric. When a voltage is applied across the plates, an electric field is created, causing positive charge to accumulate on one plate and negative charge on the other. This stored charge can then be released when needed.

Capacitance is a measure of a capacitor’s ability to store charge per unit voltage. It is defined as the ratio of the electric charge (Q) stored on each plate to the voltage (V) across the plates: C= Q/V

The unit of capacitance is the farad (F), named after the English physicist Michael Faraday. One farad is defined as the capacitance of a capacitor that stores one coulomb (C) of charge when one volt (V) is applied across its plates: 1F= 1*C/V.

**Capacitance of a parallel plate Capacitor:
** consider a parallel plate capacitor, fully charged as shown in figure.

The area of each plate M and N is say A m^{2 }and plate are separated by distance ‘d’. the relative permittivity of the dielectric used in between the plates be e_{r.}_{
}** **let C be the capacitance of parallel plate capacitor and capacitance is directly proportional to the cross sectional area of the plate and inversely proportional to the distance between the plate. So, mathematically,

CαA….. (i)

Cα1/d…(ii)

From equation (i) and (ii),

CαA/d

or, C= ε A/d

Where, ε is the permittivity of the dielectric.

ε= ε_{0 }ε_{r}

then, C = ε_{0 }ε_{r }A/ d

Where

ε_{0= }Absolute permittivity

ε_{r}= relative permittivity

**Factor affecting Capacitance**

Capacitance, the ability of a capacitor to store an electric charge, is influenced by three primary factors: the distance between the parallel plates, the area of the parallel plates, and the dielectric material placed between the plates. Let’s break down how each factor affects the capacitance:

**Distance between the two parallel plates:**

The capacitance of the capacitor is inversely proportional to the distance between the plates when the area of the plates and the materials in the gap of plates remains unchanged,

Cα1/d

this means if the distance between the plates increases, the capacitance C decrease and vice versa.

**Area of parallel plates:
**the capacitance of the capacitor is directly proportional to the area of the plates when distance between the plates and the materials in the gap of plates remain unchanged, CαA.

**Dielectric placed between the plates of the capacitor:
**the capacitance of the parallel plate capacitor is directly proportional to the dielectric constant of dielectrics when the distance between then and the area of these plates remain unchanged i.e. Cαε when A and d are constant.

**Characteristics of capacitance
**Capacitance, a key characteristic of capacitors, refers to the ability to store electrical charge. The performance and suitability of a capacitor for a specific application are determined by various parameters. Here are the main characteristics of capacitance:

**Nominal Capacitance:
**The intended or rated capacitance value of a capacitor, typically specified in farads (F), microfarads (µF), nanofarads (nF), or picofarads (pF). Determines the amount of electric charge the capacitor can store at a given voltage.

**Working Voltage :
**The maximum continuous voltage that can be applied to a capacitor without the risk of damage or failure. Ensures the capacitor operates safely within its voltage limits to prevent breakdown or degradation.

**Tolerance:
**The range within which the actual capacitance value can vary from the nominal value, typically expressed as a percentage (e.g., ±10%). Indicates the precision of the capacitor’s capacitance value, which is crucial for applications requiring exact capacitance values.

**Leakage Current:
**The small amount of current that flows through the dielectric material of a capacitor when voltage is applied, even when ideally no current should flow. Affects the efficiency and performance of the capacitor in circuits, particularly in low-power or high-precision applications.

**Working Temperature:
**The range of ambient temperatures within which the capacitor can operate reliably without performance degradation, typically specified in degrees Celsius (°C). Ensures the capacitor functions correctly in the environmental conditions of its application.

**Temperature Coefficient:
**The rate at which the capacitance value changes with temperature, usually expressed in parts per million per degree Celsius (ppm/°C). Important for applications with significant temperature variations, as it affects the stability of the capacitance value.

**Polarization:
**Refers to whether a capacitor is polarized or non-polarized. Polarized capacitors (like electrolytic capacitors) have a designated positive and negative terminal and must be connected correctly in a circuit. Incorrect connection of polarized capacitors can lead to failure or explosion, so correct polarity is critical.

**Equivalent Series Resistance (ESR):
**The internal resistance that appears in series with the capacitance, representing the losses in the capacitor. Low ESR is crucial for high-frequency and high-current applications, as it minimizes power losses and heat generation.

**Serial and parallel combination of capacitance
**

**series combination of the capacitor:**

When capacitors are connected end-to-end (i.e., the positive terminal of one capacitor is connected to the negative terminal of the next), they are in series. The overall or equivalent capacitance (C

_{eq}) of capacitors connected in series is less than any individual capacitor’s capacitance in the series.

**Formula:**

For capacitors C

_{1}+ C

_{2}+ C

_{3}+ C

_{n}connected in series, the equivalent capacitance is given by:

1/C

_{eq }= 1/ C

_{1}+ 1/C

_{2}+ 1/C

_{3}+ 1/C

_{4}+……..+ 1/C

_{n}

**Example:
**For two capacitors C1 and C2 in series:

1/C

_{eq = }1/ C

_{1}+ 1/C

_{2 }1/C

_{eq = C1. C}

_{2}

_{ /(}1/ C

_{1}+ 1/C

_{2)}

**Parallel** **Combination of Capacitors:****
**When capacitors are connected such that all their positive terminals are connected to one point and all their negative terminals to another, they are in parallel. The overall or equivalent capacitance (C

_{eq}) of capacitors connected in parallel is the sum of their individual capacitances.

Formula: C_{1}, C_{2}, C_{3}_{,} C_{n}

For capacitors connected in parallel, the equivalent capacitance is given by:

1/C_{eq }= 1/ C_{1} + 1/C_{2} + 1/C_{3} + 1/C_{4} +……..+ 1/C_{n}

**Example:
**For two capacitors (C1) and (C2) in parallel:

C

_{eq }= C

_{1}+ C

_{2}