Cell, Battery and Capacitor

Introduction to Cell

An electric cell is a device that converts chemical energy into electrical energy through chemical reactions.

A cell acts as a source of electrical energy and can provide electric current to a circuit.

Cells may be classified according to the type of electrolyte or construction used.

Examples include:

• Dry Cell
• Wet Cell
• Reserve Cell

A cell usually consists of a single electrochemical unit and is commonly used for low-power applications.

Examples include:

• Clocks
• Torches
• Remote Controls
• Small Electronic Devices

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Battery

A battery is an electrochemical source consisting of one or more cells used to store chemical energy and supply electrical energy.

A battery may contain several cells connected together.

Batteries are commonly used where greater voltage, current capacity, or longer operating time is required.

Examples include:

• Vehicles
• Inverters
• UPS Systems
• Portable Electronic Devices
• Energy Storage Systems

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Types of Cell / Battery

Batteries can broadly be classified into:

1. Primary Cell / Primary Battery
2. Secondary Cell / Secondary Battery

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1. Primary Cell / Primary Battery

A primary battery is designed mainly for single use.

It is generally not rechargeable after its stored chemical energy has been used.

A common example is a dry cell used in:

• Clocks
• TV Remotes
• Toys
• Torches

Primary batteries are generally convenient for low-power portable devices.

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2. Secondary Cell / Secondary Battery

A secondary battery is a rechargeable battery.

It can be charged again after use by supplying electrical energy in the required manner.

Because it can be charged and discharged repeatedly, it is also called a:

Rechargeable Battery

Secondary batteries are commonly used in:

• Vehicles
• Inverters
• UPS Systems
• Rechargeable Electronics
• Solar Energy Systems

Compared with many primary cells, secondary batteries may be:

• More expensive
• Heavier
• Larger
• More suitable for repeated use

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Difference Between Primary and Secondary Battery

Primary Battery	Secondary Battery
Designed mainly for single use.	Designed for repeated use.
Generally not rechargeable.	Rechargeable.
Commonly used in low-power devices.	Commonly used where repeated charging is required.
Usually simpler to use.	Requires charging arrangements.
Example: Common dry cell.	Example: Rechargeable inverter or vehicle battery.

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Combination of Cells

Cells can be connected together to obtain required electrical characteristics.

The two common combinations are:

1. Series Combination
2. Parallel Combination

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Series Combination of Cells

Cells are connected in series when the positive terminal of one cell is connected to the negative terminal of the next cell.

Representation

(- +) — (- +) — (- +)

In a series combination, the total voltage increases.

For similar cells:

Total Voltage = V₁ + V₂ + V₃ + ...

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Advantages of Series Combination

• Simple arrangement
• Higher total output voltage
• Same current passes through the series path
• Useful when a higher voltage is required

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Disadvantages of Series Combination

• A fault or disconnection may break the complete circuit.
• Total internal resistance may increase as more cells are added.

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Parallel Combination of Cells

Cells are connected in parallel when:

• All positive terminals are connected together.
• All negative terminals are connected together.

For similar cells, the output voltage remains approximately equal to the voltage of one cell, while the available current capacity can increase.

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Characteristics of Parallel Combination

• The voltage is approximately the same as that of one similar cell.
• Current demand can be shared among the cells.
• Effective internal resistance decreases when similar cells are connected in parallel.
• The combination can supply current for a longer period under suitable conditions.

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Advantages of Parallel Combination

• Useful when higher current capacity is required.
• Output voltage remains approximately the same as a single similar cell.
• Current demand is shared among the connected cells.

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Difference Between Cell and Battery

Cell	Battery
A single electrochemical unit.	One or more cells connected or packaged together.
Converts chemical energy into electrical energy.	Supplies electrical energy using one or more cells.
Usually smaller and lighter.	May be larger and heavier.
Commonly used for lower-energy applications.	Can be used for higher-energy or longer-duration applications.
Often costs less.	Can cost more depending on capacity and construction.

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Capacitor

A capacitor is an electrical or electronic component that stores electrical charge and electrical energy.

A basic capacitor consists of:

1. Two conducting plates
2. An insulating material between the plates

The insulating material is called a dielectric.

When voltage is applied across the plates:

• Positive charge accumulates on one plate.
• Negative charge accumulates on the other plate.
• An electric field is created between the plates.

The stored charge can later be released into a circuit.

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Capacitance

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

It is defined as the ratio of the charge stored on the capacitor to the potential difference across it.

Mathematically:

C = Q / V

Where:

• C = Capacitance
• Q = Electric Charge
• V = Voltage

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Unit of Capacitance

The SI unit of capacitance is the:

Farad (F)

The unit is named after Michael Faraday.

One farad is the capacitance of a capacitor that stores one coulomb of charge when one volt is applied across it.

1 F = 1 C / 1 V

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Common Units of Capacitance

Because one farad is a large unit for many electronic circuits, smaller units are commonly used.

Microfarad

1 µF = 10⁻⁶ F

Nanofarad

1 nF = 10⁻⁹ F

Picofarad

1 pF = 10⁻¹² F

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Parallel Plate Capacitor

A parallel plate capacitor consists of two conducting plates placed parallel to each other and separated by an insulating dielectric.

Suppose:

• A = Area of each plate
• d = Distance between the plates
• ε = Permittivity of dielectric
• C = Capacitance

The capacitance is directly proportional to plate area:

C ∝ A

The capacitance is inversely proportional to the distance between plates:

C ∝ 1/d

Combining these:

C ∝ A/d

Therefore:

C = εA/d

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Permittivity of the Dielectric

Permittivity can be written as:

ε = ε₀εᵣ

Therefore:

C = ε₀εᵣA/d

Where:

• ε₀ = Permittivity of free space
• εᵣ = Relative permittivity of dielectric
• A = Area of plate
• d = Distance between plates

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Factors Affecting Capacitance

The capacitance of a parallel plate capacitor mainly depends on:

1. Distance between the plates
2. Area of the plates
3. Dielectric material between the plates

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1. Distance Between Plates

Capacitance is inversely proportional to the distance between the plates.

C ∝ 1/d

Therefore:

Distance increases → Capacitance decreases

and:

Distance decreases → Capacitance increases

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2. Area of Plates

Capacitance is directly proportional to the area of the plates.

C ∝ A

Therefore:

Plate area increases → Capacitance increases

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3. Dielectric Material

Capacitance depends on the permittivity of the dielectric placed between the plates.

C ∝ ε

A dielectric with a larger relative permittivity generally increases the capacitance.

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Characteristics of Capacitors

Important characteristics used to describe a capacitor include:

1. Nominal Capacitance
2. Working Voltage
3. Tolerance
4. Leakage Current
5. Working Temperature
6. Temperature Coefficient
7. Polarization
8. Equivalent Series Resistance

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1. Nominal Capacitance

Nominal capacitance is the rated capacitance value of a capacitor.

It may be expressed in:

• Farads
• Microfarads
• Nanofarads
• Picofarads

It indicates approximately how much charge the capacitor can store for a given voltage.

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2. Working Voltage

Working voltage is the maximum voltage that should be continuously applied to a capacitor under specified operating conditions.

Exceeding the rated voltage may damage the capacitor.

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3. Tolerance

Tolerance indicates how much the actual capacitance may differ from its rated value.

It is usually expressed as a percentage.

Example:

±10%

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4. Leakage Current

An ideal capacitor would not allow current through its dielectric.

In practice, a very small current may flow through the dielectric.

This is called leakage current.

Lower leakage is important in many low-power and precision circuits.

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5. Working Temperature

The working temperature specifies the temperature range within which a capacitor can operate safely and reliably.

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6. Temperature Coefficient

The temperature coefficient indicates how much the capacitance changes when temperature changes.

This is important in circuits where stable capacitance is required.

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7. Polarization

Some capacitors are polarized.

A polarized capacitor has:

• Positive terminal
• Negative terminal

It must be connected with the correct polarity.

Electrolytic capacitors are common examples.

Incorrect connection may damage the capacitor and can create a safety hazard.

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8. Equivalent Series Resistance (ESR)

Equivalent Series Resistance (ESR) is the small internal resistance associated with a practical capacitor.

Low ESR is desirable in applications involving:

• High Current
• High Frequency
• Power Supplies

because lower ESR reduces energy loss and heating.

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Series and Parallel Combination of Capacitors

Capacitors can be connected in:

1. Series
2. Parallel

The equivalent capacitance depends on the type of connection.

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Capacitors in Series

Capacitors are connected in series when they are connected one after another along a single path.

For capacitors in series:

1/Ceq = 1/C₁ + 1/C₂ + 1/C₃ + ... + 1/Cₙ

Where:

• Ceq = Equivalent capacitance
• C₁, C₂, C₃ ... = Individual capacitances

The equivalent capacitance is smaller than the smallest individual capacitance.

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Two Capacitors in Series

For two capacitors:

1/Ceq = 1/C₁ + 1/C₂

Taking the common denominator:

1/Ceq = (C₁ + C₂)/(C₁C₂)

Therefore:

Ceq = (C₁C₂)/(C₁ + C₂)

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Example of Capacitors in Series

Suppose:

C₁ = 2 µF
C₂ = 3 µF

Then:

Ceq = (C₁C₂)/(C₁ + C₂)

Ceq = (2 × 3)/(2 + 3)

Ceq = 6/5

Therefore:

Ceq = 1.2 µF

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Capacitors in Parallel

Capacitors are connected in parallel when their corresponding terminals are connected across the same two points.

For capacitors connected in parallel:

Ceq = C₁ + C₂ + C₃ + ... + Cₙ

The equivalent capacitance is the sum of the individual capacitances.

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Example of Capacitors in Parallel

Suppose:

C₁ = 2 µF
C₂ = 3 µF

Then:

Ceq = C₁ + C₂

Ceq = 2 + 3

Therefore:

Ceq = 5 µF

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Difference Between Capacitors in Series and Parallel

Series Capacitors	Parallel Capacitors
Connected one after another.	Connected across the same two points.
Equivalent capacitance decreases.	Equivalent capacitance increases.
1/Ceq = 1/C₁ + 1/C₂ + ...	Ceq = C₁ + C₂ + ...
Same charge magnitude appears on each ideal series capacitor.	Same voltage appears across each capacitor.
Equivalent capacitance is smaller than the smallest individual capacitor.	Equivalent capacitance is larger than any individual capacitance.

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Quick Revision

Cell

A cell converts chemical energy into electrical energy.

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Battery

A battery consists of one or more electrochemical cells.

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Types of Battery

• Primary Battery
• Secondary Battery

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Primary Battery

Generally used once and not recharged.

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Secondary Battery

Rechargeable and reusable.

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Cell Combination

Series

Total Voltage = V₁ + V₂ + V₃ + ...

Parallel

Voltage remains approximately equal to one similar cell while available current capacity increases.

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Capacitor

A capacitor stores electric charge and electrical energy.

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Capacitance

C = Q/V

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Unit of Capacitance

Farad (F)

1 F = 1 C/V

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Parallel Plate Capacitor

C = εA/d

or:

C = ε₀εᵣA/d

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Factors Affecting Capacitance

• Plate Area
• Distance Between Plates
• Dielectric Material

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Series Capacitors

1/Ceq = 1/C₁ + 1/C₂ + 1/C₃ + ...

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Parallel Capacitors

Ceq = C₁ + C₂ + C₃ + ...

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Important Formulae

Capacitance

C = Q/V

Parallel Plate Capacitor

C = εA/d

With Relative Permittivity

C = ε₀εᵣA/d

Series Capacitors

1/Ceq = 1/C₁ + 1/C₂ + ... + 1/Cₙ

Two Capacitors in Series

Ceq = C₁C₂/(C₁ + C₂)

Parallel Capacitors

Ceq = C₁ + C₂ + ... + Cₙ

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Important Exam Points

• A cell converts chemical energy into electrical energy.
• A battery contains one or more electrochemical cells.
• Primary batteries are generally non-rechargeable.
• Secondary batteries are rechargeable.
• Cells can be connected in series or parallel.
• Series-connected cells can provide a higher total voltage.
• Parallel-connected similar cells maintain approximately the same voltage while increasing available current capacity.
• A capacitor stores electric charge and electrical energy.
• A capacitor contains two conducting plates separated by a dielectric.
• Capacitance is represented by C.
• C = Q/V.
• The SI unit of capacitance is farad.
• 1 F = 1 C/V.
• Capacitance increases when plate area increases.
• Capacitance decreases when plate separation increases.
• Capacitance depends on the dielectric material.
• C = εA/d for an ideal parallel plate capacitor.
• Polarized capacitors must be connected with correct polarity.
• ESR represents internal losses in a practical capacitor.
• Capacitors in series use the reciprocal formula.
• For two series capacitors, Ceq = C₁C₂/(C₁+C₂).
• Capacitors in parallel are added directly.
• Ceq = C₁ + C₂ + ... for parallel capacitors.