### Introduction

• The only particle that moves when an electric circuit is completed is the electron. For this reason, electricity is popularly described as the flow of electrons.
• In the atom, there are 3 fundamental particles – proton, electron, and neutron.
• The proton and neutron give the atom its mass.
• The proton and electron are collectively designated as electrical particles because each is surrounded by an invisible field of force that reacts in an electrically negative or positive manner (respectively) with the adjacent matter. This gives the electron a negative charge, while the proton is given a positive charge.
• The mass of the proton is 1800 times the mass of the electron, but each electrical particle has a unit (one) electric charge, i.e + and -. This means that for an equal mass of protons and electrons, there will be 1800 more negative charges as compared to positive charges.
• The basic law of charges:
• Like charges repel, Unlike charges attract.
• Because of differences in mass, the proton remains stationary when it attracts the electron, which implies that only the electron moves. This ordered flow of electrons is described as the flow of current. Likewise, in terms of the mass-to-charge ratio, the electron has a stronger field of force than the proton.
• When an atom loses or gains an electron it becomes an ion. If it loses an electron, it becomes a positive ion. If it gains an electron, it becomes a negative ion.
• The power of the invisible field of force around an electrical particle (i.e proton or electron) is called the field strength. This field strength varies inversely with the distance of the field from the electrical particle using this proportion:

Field Strength α 1/(distance squared)

• The field strength of electrical particles is directly proportional to the number of these particles.
• The invisible field around an electrical particle is called its electrostatic field. When an electron moves, then it moves with its electrostatic field, and this moving field creates the dynamic electricity. To cause this electron to move, it needs to be pushed by a negative field strength, or be pulled by a positive field strength.

### Atom and its Orbital Shells

• Matter that is made up of only one type of atom is called an element, but if it is made up of two or more different atoms, then it is called a compound.
• In the atom, the electron orbits around the nucleus – which is made up of protons and neutrons (except for the hydrogen atom). This orbiting electron is called an orbital or planetary electron. The lithium atom has 3 planetary electrons orbiting around a nucleus made up of 3 protons (colored red) and 3 neutrons (colored blue).
• Each atom has orbital shell(s) depending on the number of electrons, and the further the electron is from the nucleus, the less strongly it is bound to the nucleus. Thus, the electron in the outermost orbital is least strongly bound to the nucleus as compared to the electron in the innermost orbital shell.
• The orbital shell that surrounds the nucleus can hold 2 electrons and is called the innermost shell, and the shell surrounding this innermost shell can hold a maximum of 8 electrons, and the next outer shell can hold 18 electrons.
• The electron that is tightly bound to the nucleus is called the valence or bound electron, while the loosely bound electron in the outermost orbit that can move away from the nucleus is called the free electron. To move this free electron, there is a need for energy input to overcome the resistance of the nucleus to allow for the escape of this electron.
• Heavy atoms are usually unstable and decompose to form stable atoms. The atom that undergoes decomposition by emitting energy is called a radioactive atom.

### Current, EMF, and Resistance

• Current (I) flows in a conductor if enough electron-moving force is applied to cause an ordered flow of electrons. This electron-moving force is called electromotive force (EMF) (or electric pressure, electric potential, or potential difference [PD]), and its unit of measurement is the Volt (V).
• The unit of measurement of current is Ampere (A).
• When EMF is applied to create a current flow, there is an opposing force to this current flow in the conductor, and this opposing force is called resistance (R), and its unit of measurement is Ohm (Ω).
• The ampere is the number of electrons orderly flowing through a point in a circuit in one second, and this number of electrons is measured as Coulomb (C). One C is 6.25 × 1018 electrons, and 1 Coulomb-per-second is called an Ampere.
• Any material without free electrons cannot conduct current and is thus called a non-conductor or insulator. Likewise, any material with an abundance of free electrons can conduct current, and is thus called a conductor. Glass is a good insulator, while silver is a good conductor.
• There are 4 types of current:
• Direct current (DC): The current flows in the same direction with no variation in its strength (amplitude) and EMF.
• Varying DC: This is a direct current whose current and voltage vary, though neither falls to zero.
• Pulsating DC: This is a direct current whose current and voltage vary, with either periodically falling to zero.
• Alternating Current (AC): The direction of ordered electron flow reverses periodically, and this is associated with changes in current amplitude.
• The simple electric circuit has 4 main components:
• The source of EMV.
• Conducting wires.
• Load that consumes electrical energy.
• Control device, usually a switch, that opens or closes the circuit.
• The resisting ability of a wire is determined by the following 4 physical attributes:
• The material the wire is made of.
• The length of the wire.
• The temperature of the wire.
• The cross-sectional area of the wire.
• Resistance in the wire can be calculated using this formula:

Resistance (in Ω) = ρ (resistivity of material) × Length (in meters) / Cross-sectional Area

R= ρL/A.

• ρ is the resistivity of the material of the wire, and its unit of measurement in ohm-meter (Ωm).
• The reciprocal of resistance is called conductance, which is a measure of the ease of current flow in a material.
• Conductance (G) is calculated as 1/R and its unit of measurement is the siemens (S).
• The best conductor of electricity is silver, and for this reason, it has been assigned the relative conductivity value of 100%. This allows other conductors to have their conductivity measured in relation to silver e.g copper has a relative conductivity of 96%. Gold and aluminum have relative conductivity of 73% and 59% respectively.

### Electrical Power

• Ohm’s Law postulates that current is directly proportional to the applied voltage, and inversely proportional to resistance. This is expressed as:

Current = Voltage/Resistance, or I=V/R, which can be transposed to get;

V=IR

R=V/I

• Volts push Amps through Ohms i.e EMF generates current flow against resistance.
• Electrical power is measured in terms of the Watt (W), with 1W being equal to work done by 1V to move 1C of electrons for 1 second (s), i.e 1W = 1VC/s. Also, 1C/s = 1A, therefore 1W=1VA. This means that power can be calculated as:

Power (P) = Voltage (V) × Current (I).

If V=IR is substituted for Voltage, then P = IR × I = I2R.

If I=V/R is substituted for Current, then P = V × V/R = V2/R.

• 1 horsepower (HP) is equal to 746 Watts.
• Work is described as power used for a specific time period. This allows for amount of work to be calculated as follows:

Work = Power × Time (in seconds), which means that,

Power = Work/Time

• The above formula shows that if 1W of power is used for 1 second, then the work done is:
• Work = 1W × 1s = 1W.s (or 1 Joule).
• The Joule (J) is the unit of measurement of work.
• In the circuit, work is done by the ordered flow of electrons. The work done by these electrons is measured using the electron volt (eV), which can be calculated as follows:

1 Joule = 1W used for 1 second = 1VC/s × 1s = 1VC (Volt-Coulomb).

Because 1C is 6.25 × 1018 electrons, then 1 Joule = 1V × (6.25 × 1018) electron-volt (eV) = 6.25 × 1018 eV.

• Electricity providers charge for work done using their electricity, and this is charged as Kilowatt-hours (kWh), which makes it a key unit of energy.
• 1 kilowatt-hour is equal to:

1 kWh = 1000 watt × 3600 seconds (or 1hour) = 3.6 × 106 Joules = 3.6 megaJoules = 3.6MJ.

### Earth Return and Electric Shock

• Electric shock is the sudden involuntary contraction of skeletal muscles caused by current flow through the body after a person touches a live wire hence completing a circuit. It can cause pain and severe burns if one touches a high-voltage wire. The human body has a resistance value range of 10-50 kΩ. At 9mA and 6mA for an adult male and female respectively, the electric shock causes significant discomfort to cause each to release the live wire.
• Planet earth can be used as a conductor. The circuit where the earth is used to connect the load to the power source is called the earth return.

### Voltage Drop and the Power Transmission Grid

• When current flows through a resistance, power is dissipated and this leads to a drop in the EMF, and this is known as voltage drop. This means that the voltage at either end of the resistive load will have different voltage values.
• By derivation, Ohm’s Law reveals that resistance is directly proportional to voltage drop and inversely proportional to current. This has an application in the national grid.
• During power transmission, the power generated at the power station goes through a step-up transformer and its voltage is increased to about 330,000 volts, which is then fed into the transmission lines. The transmission lines convey this high voltage electricity to substations where it is stepped down to voltage levels that can be used in homes or industries, which is about 110V-220V and 415V respectively. The reason for stepping up the voltage before transmission is to reduce the current during power transmission while allowing for minimal voltage drop thus ensuring that power losses during the transmission of electricity as kept at a minimum.

### Static Electricity

• Static electricity is created when two objects rub together thus allowing electrons to flow from one object to another. This results in a buildup of electrons in one object and the depletion of electrons in the other. As expected, this creates a charged electrical field between the bodies with one body being negatively charged and the other body is positively charged.
• This electrical field possesses a potential force because the electrons can flow to a positively charged body. This potential is expressed as voltage, but because there is no flow of electrons, then there is no current generated. In other words, this charged electrical field possesses electromotive force but cannot generate current.
• Static electricity is accurately described as electricity only when there is a flow of electrons, but popular use acknowledges charged bodies as possessing the potential of static electricity.
• If a flow of electrons occurs, then an arc can be generated due to the high current generated. This is seen during a lightning strike. It is this type of arcing that caused the gasoline/petrol tank to explode in the early 1900s until mechanics attached metallic chains to these tanks so as to create a short circuit that allowed charges that had built up inside the tank to flow to the road.
• Static electricity can be generated when two non-conducting materials are rubbed together.
• The lightning strike is an example of a sudden discharge of static electricity. The clouds that are moved around (i.e mobilized) by wind (i.e moving air) are able to pick electrons from the trees, buildings, ground, and any charged body. The size of the cloud determines the number/amount of electrons it can pick and hold, and the cloud can hold as many electrons as its mass allows. This means that the bigger the cloud, the more powerful the lightning strike it can generate.
• Charge buildup in the cloud generates of very high potential difference (voltage) between the cloud and the ground, and when the cloud cannot hold any more electrons, it discharges this voltage as a lightning strike. As expected, this strike carries a very high current that explains why it (lightning strike) can kill a person, set trees on fire, and cause an electrical surge in electrical appliances after it hits a building.
• The electrical surge caused by a lightning strike is due to the sudden addition of large amounts of currents into the powerlines, which is then transmitted downstream to electrical appliances connected to this grid. This sudden spike in current can occur directly when the distribution or powerlines are struck by lightning and this is called direct lightning. Likewise, if the lightning bolt strikes near the powerlines, it crosses their electromagnetic fields and this causes sudden changes in these fields which in turn induces a current in the wires, and this is called induced lightning. At times, the lightning bolt strikes far away from the powerlines and is discharged into the ground, but due to how powerful the strike was, it raises the ground potential thus causing current to flow from the ground through the earth return path back to the house where it is discharged through the socket onto connected appliances. This discharged current is called the backflow lightning current.
• The induction of large amounts of current into the transmission lines by a bolt of lightning leads to the generation of large amounts of voltages according to Ohm’s Law. This generated voltage is called induced voltage, and it increases the voltage that reaches electrical appliances. If this increased voltage exceeds the upper limit of the AC voltage capacity of the appliance, then it is described as an overvoltage. This overvoltage increases the power delivered to the appliance hence the power surge. For example, if lightning generates an overvoltage of 400V in a 240V AC line, then the standard 13A fuse of an electrical appliance will allow 5200W of power to be delivered to this appliance instead of the normal 3120W or the upper power limit of 4400W that the appliance can withstand.
• Because this voltage is generated by lightning, it is described as overvoltage of atmospheric origin. This overvoltage can be caused by a lightning bolt that struck miles away from the affected house.
• Another phenomenon related to static electricity is the electric shock felt by the driver and the toll collector during payment of the toll using cash. This only occurs when the driver drives a car on a toll bridge and then pays for the toll after crossing this bridge. This allows the car to pick up electrical charges from the road, and then transfer these charges to the body of the driver. Discharge occurs when the driver hands over cash to the toll collector, and this sudden electrical discharge is felt as an electric shock. To manage this situation, drivers have been mandated to pay the toll before crossing the bridge, and engineers have installed protruding wire or metal sheets that can be struck by the vehicle thus allowing for the safe flow of the charges from the car to the road which results in an audible zap sound.

### Circuit

• In a series circuit, the current is constant around the circuit and total resistance is the sum of individual resistances of the loads which can be calculated as:

RTotal = R1 + R2 + R3 + Rx….

• In the series circuit, the voltage drops as it passes through a resistance/load, and the total sum of these voltage drops equals the applied voltage. Therefore, 2 or more loads connected in series act as voltage dividers.
• Regarding power in the series circuit, the power dissipated in each load should add up to the total power provided by the source. Thus, the power dissipated can be calculated as:

Power Total = PowerR1 + PowerR2 + PowerR3 + PowerRX…..

• Each parallel path in a parallel circuit is called a branch, and each branch has its own current, though all branches have the same voltage. The sum of branch current equals the total current drawn from the source, and this is calculated as:

Current (I)Total = I1 + I2 + I3 + IX…..

• The total resistance in a parallel circuit can be calculated using this equation:

1/Resistance(R)Total = 1/R1 + 1/R2 + 1/R3 + 1/RX….

• The combination of all the branches in the parallel circuit is called a bank.
• In the series-parallel circuit, some components are connected in series if there is a need to ensure that the same current flows through them, while other components are connected in parallel to ensure that the same voltage flows through them.

### Magnetism

• The flow of current through a metallic conductor creates a magnetic field around the conductor. This magnetic field is oriented perpendicularly to the direction of the current flow.
• The strength of this magnetic field is inversely proportional to the distance away from the conductor.
• If the conductor is looped, the magnetic field is concentrated in the looped core.
• If the conductor is turned into a coil, then the magnetic field is concentrated around the coil, and if the number of coils is sufficiently high, then an electromagnet is produced. This type of electromagnet is called an air core electromagnet because it is formed by the electrical wires only. If these wires are coiled around a ferrite core that can be easily magnetized and demagnetized, e.g soft iron, then a soft magnet is created when this iron is magnetized by the magnetic field.
• The magnetic fields in the electromagnet are held closer to the coil if the electromagnet has an air core. However, if an iron core is introduced, the flux density of the magnetic fields increases as the iron allows the lines of force to be distributed throughout its volume. This ability to concentrate the lines of force of the magnetic field in a material other than the core is called permeability. Conversely, the property of a material to not be affected by lines of magnetic force is called reluctance.
• Permeability is represented using the symbol μ. Air has a permeability value of 1.
• According to the atomic theory of magnetism, atoms in nickel, iron, and cobalt are arranged into magnetic entities called domains.
• Each domain has one of three directions of magnetization: hard magnetization, easy magnetization, and semi-hard magnetization.
• When this material is placed in a weak field of magnetic force, the domains align themselves in the easy magnetization direction, which means that they will lose their aligned orientation when the force is removed. If the force is increased, then the domains are aligned in the semi-hard direction, which implies that some domains are aligned in the hard direction while others are in the easy direction; and when the force is removed, those domains aligned in the easy direction lose their orientation, while those aligned in the hard direction keep their orientation.
• The degree of magnetism retained after the external magnetizing force is removed is called residual magnetism. When enough force is applied to align all the domains in the hard direction, then the iron is described as being magnetically saturated. This ability to retain magnetism after the external magnetic field is withdrawn is called remanence.
• Any element that has, or can have, domains is called a ferromagnetic element. Non-ferromagnetic materials are categorized into two broad groups depending on how they behave when they are placed in a magnetic field:
• Paramagnetic Material: Its atoms line up with the magnetic field.
• Diamagnetic Material: Its atoms are not aligned to the magnetic field, with most atoms aligned perpendicularly to this field.
• Ferromagnetic material with a high remanence value, e.g Alnico, is used to create a permanent magnet. Relatedly, the ferromagnetic material with a low remanence value such as permalloy or pure iron, is used to create a temporary magnet.
• A ferrite core is made up of finely powdered iron held together by a non-conductive binder.
• The permanent magnet can lose its magnetism when heated, and the temperature at which this loss occurs is called the Curie temperature.
• If a permanent magnet is placed inside a soft iron box, then all its magnetic lines of force are contained within the box and no external field is produced. This is called magnetic shielding.