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Category: Physics

  • what is Domestic wiring

    what is Domestic wiring

    Domestic wiring refers to the electrical wiring within a residential building. It encompasses the components and circuits that provide power for lighting, appliances, and other electrical needs. In domestic wiring, we studies: installation and connection of wires, switches, outlets, and other electrical devices. Understanding domestic wiring, ensures safe and reliable power supply.

    what is domestic wiring

    Domestic wiring refers to electrical connections that allows use of electric powers supplied by power providers .

    Electrical power is usually supplied at 240V after the high voltage transmitted is scaled down through a local transformer. The high voltage transmission from power source could be 11000 V or more. The consumer will need only 240 V, therefore a step-down transformer will be needed.

    Electric power is connected to a homestead from the transformer by use of two-wire cable. One cable is earthed at the transformer. The earthed wire is referred to as the neutral wire .

    The earthed considered to be at zero electrical potential while the other wire is referred to as the live wire. The cable goes through the electrical company fuse box . The live wire is connected to a 60 A or high fuse value. The cable is then connected to the power meter where energy consumption is registered. From there it passes on to the consumer’s fuse box as illustrated.

    consumers fuse box in domestic wiring

    It is the central part of an electrical system. It distributes electrical power and provides circuit protection. The figure below illustrates a common fuse box connections in a domestic wiring.

    Consumers fuse box

    Here’s an overview of what it includes and what you should know:

    The main switch

    This is a double -pole switch which disconnects both the live and the neutral wire at the same time. disabling all the circuits in the house when needed. It is the main connecting link between external supply and household wiring . however, but we can have more than one mains switch.

    The live busbar

    This is a brass bar to which all live wires and the fuse are connected to. It connects to the live wire through the main switch. It connects the live wire of each circuit through a fuse.

    Neutral busbar

    This is the brass bar to which all neutral wires are connected to in domestic wiring.

    Earth terminal

    It is the earthed cable in the fuse box connected to the thick copper bar buried deep in the earth. It can also be earthed through water piping.

    fuses

    They are made of short thin wire mostly an alloy of cooper and tin. The alloy wire should have a low melting point. Fuses are used to safeguard against excess current in the circuit. When current exceeds the fuse rating, the wire gets very hot and melts hence disconnecting the circuit.

    The melting disconnects the excess current which would have otherwise damaged the electrical appliances. Fuses also reduces risk of fire incase there is overheating in a circuit.

    a fuse used in domestic wiring
    An electric fuse
    fuse symbols as used in domestic wiring
    fuse symbol (old)
    fuse standard symbols as used in domestic wiring
    fuse standard symbols

    The circuit breaker

    Circuit breakers are preferred over fuses protect electrical components from excessive flow for current.

    When excess current flows through the circuit, increased magnetic power of the electromagnet opens the switch. This stops electric current flow. Once the problem causing the excessive current flow has been corrected , the switch is closed by mechanical means.

    An advantage of circuit breakers over the fuses is that the circuit is broken simultaneously where the fuse melts slowly. The circuit breaker reset itself once the electric surge is corrected. This is unlike fuse that need to be replaced when it’s fuse wire melts.

    common symptoms of electrical problems in domestic wiring

    • repeatedly Tripping circuits
    • Burning smell or scorch marks
    • Buzzing sounds

    Distribution of power from the consumers unit

    House wiring systems distribute electricity throughout a building. Common systems include cleat, casing & capping, batten, lead sheathed, and conduit wiring. conduit is considered the most popular and safest, involving pipes (metal or PVC) to house wires.

    consider the setup below:

    Each component is has a wire running from the live busbar through an appropriate fuse or circuit breaker. There is also a return wire running from the neutral busbar to the output terminal.

    Except for the lighting circuit, other circuits have an earth connections running from the earth terminal to the socket. Appliances that requires earthing are automatically earthed through the socket making them safe to handle. Not earthing some appliances exposes danger to the consumer because they can be shocked while using them.

    The lighting circuit

    In lighting circuit, lamps are connected in parallel so that they operate at the same mains voltage and also operate independently. Switches are placed on live wire for safety purposes.

    If the switch was on neutral wire, the wire would still be connected to the mains potential even when the switch is off. This would cause an electric shock when one handles any conductor linked to the live wire.

    since lighting circuit carries relatively low current, the wire used is relatively thinner than those of other circuits. In an ordinary house, power for the lighting is usually supplied through 5A fuse .This is because each lamp takes only a small current.

    The two ways switch circuit

    A two-way switch circuit allows a lamp or other electrical device to be controlled from two different locations. This is achieved by using two or more switches that are connected in a specific way.

    In this circuit, an electric lamp can be operated by any one of the two switches. The circuit allows a bulb to be put on by one switch and be put off by the other switch.  The most common application is for controlling staircase lights from both the top and bottom of the stairs. A switch at the bottom of the staircase can be used to put on the light. The switch on the top of the staircase then turns it off. A lamp can be turned on by a switch at the door. Another switch at the other end of the room turns it off.

    Figure below illustrates a two way switch:

    when the contact is made at poles A and B as illustrated on the diagram, the bulb lights. The same thing happens when contact is made at C and D simultaneously.

    To put off the bulbs at point P, the switch is made to make contact at C while Q is in contact with B. To put on the bulb again at Q, the switch is made to contact D. At that point, P and C are in contact with each other.

    The ring mains circuit

    A ring main circuit, also known as a ring circuit. is a type of electrical circuit used in many UK homes to distribute electricity to power sockets. It’s characterized by a looped cable that runs from the consumer unit (fuse box), through multiple sockets, and back to the consumer unit. This looped design allows electricity to reach a socket from either direction, reducing the load on the cable compared to a single-direction radial circuit

    The figure below illustrates the ring mains circuit.

    The power for the sockets in the various rooms is tapped at convenient points from the loop. The lop arrangement of the cable enables a double path for the current. The loop arrangement also effectively increases the thickness of the wire used. This reduces the risk of overloading the circuit when several sockets are in use.

    Appliances using the ring main circuit are provided with a third wire connected to the casing. From the power socket, the third wire links with the earth terminal at the consumer unit through the mains circuit earth wire. If the live wire accidentally touches the casing, it makes it live. A large current flow through the earth wire. The large current will causes the fuse to blow, cutting off the current. Anyone handling the appliance will thus be safe from possible shock.

    The cooker circuit

    A cooker circuit refers to the electrical circuit dedicated to powering an electric cooker. Typically a hob and oven, in a domestic setting. It’s designed to handle the high power demands of cooking appliances. It usually involves a dedicated circuit breaker, a cooker control unit (CCU) and specific wiring configurations.

    he cooker circuit in domestic wiring

    The cooker circuit has the same connection and design with water heater circuit. They are both supplied with own electric circuits. These are earthed and their wires are relatively thicker than those for the lighting circuits as they carries large currents.

    The three pin plug

    A three-pin plug is a type of electrical plug used to connect an appliance to the power supply. It has three metal pins (or prongs) that fit into matching holes in a socket. A three pin plug connects appliances to power source through a socket.

    A three-pin plug has three terminals labeled L, N and E. They represent live, neutral and earth pins respectively. The three leads from the appliances are connected to the three pins as shown:

    The three pin plug with their insulated leads

    The insulation on the three leads on the power circuit are colored differently. This enables us link correctly when connecting to the power circuit. The live wire is colored red or brown. The neutral wire is colored blue or black while the earth is colored green or green with yellow stripes.

    The three pin plug circuit is represented as shown on diagrams:

    Three-pin plug
    The socket for three-pin plug

    A fuse is used in the plug to safeguard the appliance from the damage due to excessive current in the circuit. The rating of the fuse depends on the operating current of the appliance. The value of the chosen fuse should always be slightly above the value of the operating current of the appliance. An appliance operating at 4 A will need about 5A fuse as the most appropriate fuse. An 13 A fuse would be suitable for an appliance of around 11 A.

    Example problem

    A building has a lighting circuit operated from the 240V mains supply.20 bulbs rated 10w 240v are switched on at the time. what is the most suitable fuse for the circuit.

    solution

    Power = voltage(V) x Current(I)

    $$current(I) = \frac{20P}{Voltage(V)}$$ $$ = \frac{20 x 10}{240}=0.8333$$ $$\text{Hence the most suitable fuse for the circuit is a 1.0A fuse}$$

    Related topics

  • Rectilinear Propagation of waves

    Rectilinear Propagation of waves

    Rectilinear Propagation of waves means straight line travel of waves. It is a property that describes wave as traveling in a straight lines and perpendicular to the wavefront.

    To illustrate rectilinear propagation of waves, consider the ripple tank that is set to produce plane waves.

    Two rulers are placed underneath the tray of the ripple tank.  They are parallel to each other and perpendicular to the bar so that the waves produced are plane waves.

    Consider the setup below;

    Illustrating rectlinear Propagation of waves in a ripple tank

    When we start the vibrator and adjust it to the appropriate frequency, the wave fronts are perpendicular to the wavefront.

    If we replace the straight bar attached to the vibrator with a small ball, the vibrator produces circular waves that propagates as illustrated below.

    We can then adjust the rulers beneath the tray such that they are perpendicular to the wavefronts. We see that the circular waves moves outwards from the source and always perpendicular to the wavefronts.

    From here we see that waves are propagated along straight lines.

    Wavefronts

    A wavefront is an imaginary line which joins a set of particles which are in phase for a wave in wave motion . While observing wave motion in a ripple tank, wavefronts can be seen on the white paper. The formation of circular wavefronts and plane wavefronts are as shown.

    Circular and plane wavefronts

    A ray in wave propagation

    A ray is an idealized line that represents the direction of energy flow or wave propagation in a medium.

    In waves, a ray is a line drawn perpendicular to the wavefront showing the direction of travel of the wave energy. See the figure below

    The figure shows that the direction of wave travel is perpendicular to the direction of vibration.

    Other topics

  • Exam Questions on Thin lenses

    Exam Questions on Thin lenses

    This lenses operates from the principles of light refraction(bending) when the medium of transmission changes. Questions on thin lenses test several important physics concepts. These include:

    1. Refraction of Light

    • Bending of light when it passes from one medium to another
    • How curved surfaces (lenses) change the direction of light rays.
    • Application of Snell’s Law (conceptually, even if not directly calculated).

    II . Image Formation

    Understanding how images are formed by:

    • Convex (converging) lenses
    • Concave (diverging) lenses

    A learner must know:

    • When images are real or virtual
    • if images formed upright or inverted
    • Whether image formed is
    • magnified or diminished

    III. Ray Tracing Principles

    Use of the three principal rays:

    • Ray parallel to the principal axis
    • Rays through the optical centre
    • Ray through the focal point

    This tests geometric understanding of light behavior.

    iv. Lens Formula (Mathematical Relationship)

    1f=1v+1u\frac{1}{f} = \frac{1}{v} + \frac{1}{u}Tests:

    • Algebraic manipulation
    • Substitution and rearrangement
    • Use of correct sign convention

    v. Magnification

    M=vuM = \frac{v}{u}M=uv​

    orM=hihoM = \frac{h_i}{h_o}

    Tests:

    • Proportional reasoning
    • Understanding of image size relationships

    vi. Graphical Skills

    Some questions require:

    • Scale diagrams
    • Plotting graphs
    • Determining focal length from graphs

    vii. Experimental Skills

    Students may be tested on:

    • Determining focal length experimentally
    • Sources of error
    • Drawing conclusions from results

    viii. Concept of Proportionality

    Especially in experiments relating object distance, image distance, and focal length.

    Some examination Questions on Thin Lenses

    Question 1 (Thin lenses)

    1. (a) State the meaning of the term “principal focus” as applied in thin lenses. (1 mark)
    2. (b)  you are provided with the following apparatus to determine the focal length of a lens:

    -a biconvex lens and lens holder.

    -a lit candle

    -a white screen.

    -a metre rule

      (i) Draw a diagram to show how you would arrange the above apparatus to determine the focal length of the lens (1 mark)

    (ii) Describe the procedure you would follow.    (1 mark)

    (iii) state two measurements that you would take      (2 marks)

    (iv) Explain how the measurements in (iii) would be used to determine the focal length.             (2 marks)

    (c) An object is placed 30 cm infront of a concave lens of focal length 20 cm. Determine the magnification of the image produced.                   (4 marks)

    Question 2

    (a) state 2 applications of convex lenses      (2 marks)

    (b) A form 4 student did an experiment on thin lenses by varying the object distance and recording the corresponding image distance for the formed by the lenses in an attempt to determine the focal length.

    Object distance u (cm)Image distance V (cm)UV (cm2)(U+V)cm
    1530  
    2020  
    2516.7  
    3015  
    4013.3  
    6012  

    On the grid provided, plot the graph of uv against u+v  (5 marks)

    A grid to draw ray diagram for image formed by thin lens

    Related topics

  • High Voltage Power Transmission and Power Losses

    High Voltage Power Transmission and Power Losses

    High voltage power transmission systems are designed to transport electrical power over long distances while reducing power losses caused by resistance in transmission cables. By increasing voltage and lowering current, power companies can deliver electricity more efficiently, safely, and reliably. This process plays a major role in modern power grids and helps ensure stable electricity supply across cities and rural areas.

    In this article, you will learn how high voltage power transmission works, why power losses occur during transmission, the importance of transformers in reducing energy wastage, and the dangers associated with high voltage lines. You will also explore practical examples and calculations that explain how electrical engineers minimize power loss in transmission systems.

    Whether you are a physics student, engineering learner, teacher, or simply curious about electricity transmission, this guide will help you clearly understand the science behind high voltage power transmission and power losses.

    Electricity generated at power stations must travel long distances before it reaches homes, industries, schools, and businesses. To make this possible efficiently, electrical power is transmitted using high voltage transmission lines. High voltage transmission helps reduce energy losses and ensures reliable delivery of electricity over large distances.

    High voltage power transmission flow diagram
    • Electricity is generated at power stations.
    • Voltage is stepped up for efficient long-distance transmission.
    • High voltage reduces power losses in transmission cables.
    • Substations step the voltage down before distribution to consumers such as homes, industries, schools, and businesses.

    What is High Voltage Transmission?

    High voltage transmission is the process of carrying electrical power over long distances using very high voltages such as 110 kV, 220 kV, 400 kV, or even 765 kV. Transmitting electricity at high voltage reduces the amount of energy lost as heat in the transmission cables.

    Power stations usually generate alternating current (AC) electricity at voltages between 11 kV and 25 kV. Before the electricity is transmitted, transformers are used to step up the voltage to much higher levels, typically between 132 kV and 400 kV.

    The electricity is then transmitted through overhead power lines to substations, where the voltage is stepped down for safe distribution to consumers.

    Different consumers require different voltage levels:

    • Heavy industries may require voltages above 30 kV
    • Light industries may use around 10 kV
    • Homes and domestic users usually require 240 V
    High voltage power transmission cables
    power transmission cables

    How Power is Distributed

    The transmission and distribution process follows these stages:

    1. Electricity is generated at the power station.
    2. A transformer steps up the voltage for long-distance transmission.
    3. Electricity travels through high voltage transmission cables.
    4. Substations step down the voltage.
    5. Electricity is distributed to homes, industries, and businesses at suitable voltage levels.

    Why High Voltage Reduces Power Loss

    Electrical cables have resistance, and this resistance causes some electrical energy to be lost as heat during transmission.

    The power loss in transmission lines is given by:

    P=I2RP = I^2RP=I2R

    Where:

    • P = power loss
    • I = current flowing through the cable
    • R = resistance of the cable

    From the formula, power loss increases when current increases. Therefore, reducing current reduces energy losses.

    Since electrical power is also given by:

    P=VIP = VI

    For the same amount of power, increasing the voltage allows the current to decrease. This is why electricity is transmitted at very high voltages and low currents.

    Methods Used to Reduce Power Losses

    Power companies use several methods to minimize losses during transmission:

    1. Stepping Up Voltage

    Transformers increase the voltage before transmission. Higher voltage means lower current and therefore lower power loss.

    2. Using Thick Transmission Cables

    Thicker cables have lower resistance, which reduces heat losses.

    3. Using Good Conductors

    Transmission cables are made using materials with low electrical resistance.

    Why Aluminum is Preferred for Transmission Cables

    Aluminum is commonly used in transmission lines because:

    • It is a good conductor of electricity
    • It is lightweight
    • It is cheaper than many other conducting materials

    Dangers of High Voltage Transmission

    Although high voltage transmission is efficient, it also presents several risks:

    • Electric shock if cables fall or hang too low
    • Fires caused by loose or damaged cables
    • Strong electric fields that may affect nearby communities
    • Lightning strikes causing surges in electrical systems
    • Cables touching during strong winds and causing sparks or fires

    Proper maintenance and safety measures are therefore very important.

    Example Problem

    A transmission cable has a resistance of 100 Ω and carries electricity at 10 kV with a current of 1.0 A. The voltage is stepped up to 18 kV using a transformer.

    Determine the power loss after stepping up the voltage.

    Solution

    Assuming the transformer is 100% efficient:

    Step 1: Use the transformer power relationship

    VpIp=VsIsV_p I_p = V_s I_sVp​Ip​=Vs​Is​

    Substituting the values:

    • Primary voltage = 10,000 V
    • Primary current = 1.0 A
    • Secondary voltage = 18,000 V

    10000×1.0=18000×Is10000 \times 1.0 = 18000 \times I_s10000×1.0=18000×Is​ Is=1000018000I_s = \frac{10000}{18000}Is​=1800010000​ Is=0.556 AI_s = 0.556\ AIs​=0.556 A

    Step 2: Calculate Power Loss

    Using:P=I2RP = I^2RP=I2R P=(0.556)2×100P = (0.556)^2 \times 100P=(0.556)2×100 P≈30.9 WP \approx 30.9\ WP≈30.9 W

    Without Stepping Up the Voltage

    P=(1.0)2×100P = (1.0)^2 \times 100P=(1.0)2×100 P=100 WP = 100\ WP=100 W

    This shows that stepping up the voltage significantly reduces power loss.

    Practice Question

    A generator produces 750 kW at a voltage of 15 kV. The voltage is stepped up to 125 kV and transmitted through cables with a resistance of 500 Ω.

    Assuming the transformers are 100% efficient, calculate:

    1. The current produced by the generator
    2. The current flowing through the transmission cables
    3. The voltage drop across the cables
    4. The power lost during transmission
    5. The power reaching the substation

    Conclusion

    High voltage transmission is an essential part of modern electrical power systems. By transmitting electricity at high voltage and low current, power companies minimize energy losses and improve efficiency over long distances.

    Transformers play a key role in stepping voltage up for transmission and stepping it down for safe use by consumers. Despite the dangers associated with high voltage lines, proper design and maintenance make power transmission both efficient and reliable.

    Related topics

  • Simple Electric Circuits

    Simple Electric Circuits

    Electric circuits are pathways through which electric current flows. We can make simple electric circuits using simple apparatus and procedure.
    An electric current is the flow of electric charge through a conductor, such as a wire. It occurs when charged particles move. Typically, electrons respond to an electric field created by a voltage difference across the conductor. Voltage difference is provided by a cell or a battery.

    A cell is a device that converts chemical energy into electrical energy, providing a source of electrical power. It consists of one or more electrochemical reactions that generate a flow of electrons, which is the electric current. A battery is a combination of two or more cells.

    The figure below shows a dry cell that is common in making of many simple circuits.

    showing Simple Electric Circuits
    a dry cell

    The figure below three dry cells connected to make a battery:

    simple electric circuit using battery of three cells
    battery of cells

    Cell provides the energy required to pump electrons in a conductor so that they can move in a closed loop. A cell creates voltage difference by creating a region of excess electrons on one side and deficit of electrons on the other side through chemical reactions. A conductor is connected such that it runs from one side of the cell to the other in a closed loop.

    When there is no gap between the two ends of the cell or battery along the conductor, the circuit is said to be complete. Charge flows only when the circuit is complete. Cell acts as the pump to push the charges along the conductor so that they can be on the move.

    The end of battery with excess of negative charge is called the negative terminal. The other end with with deficit of charge is known as the positive charge. Charge flows from negative terminal of a cell towards the positive terminal. Current flows in opposite direction conventionally form positive terminal of the battery towards the negative end. Current is when charges flow and is a function of the speed of flow of charges. Infact the formal definition of current is that current is the rate of flow of charges. The standard international unit of current is called Ampere (A).

    From the definition of current:

    Current(I)=charge flowing through a section of conductor per unit time(t)

    I=Qt where I is the current and Q is the amount of charge flowing

    charge is measured in coulombs while time is in seconds. Therefore Ampere is the number of coulombs per second.

    Example:

    What is the current flowing through a bulb where 100 coulombs of charge is observed to flow for 1.8 minutes?

    solution

    I=Qt

    =10060×1.8=100108=0.926 A

    Example 2:

    what amount of charge is flowing through a conductor where current flowing is 6.0 A

    solution

    I=Qt=Q x 1 second

    6.0=Q x 1 second

    Q = 6.0 coulombs

    Making of Simple Electric Circuits

    A simple electric circuit consists of a few basic components arranged in a loop that allows electric current to flow. The most basic components of a simple circuit includes:

    Power Source

    This is typically a battery or a cell that provides the electrical energy to push the charge around the circuit. The positive and negative terminals of the power source create a voltage difference that drives the current.

    Conductor

    These connect the components of the circuit and provide a path for the current to flow. The most common material to make conductors is copper wires. Other useful material to make electric current is aluminum wire. other wise most of metallic materials can conduct electric current.

    Load

    A load is any component that uses electrical energy. It performs a function, such as a light bulb, motor, or resistor. The current passes through the load, and energy is transferred to it (e.g., light or heat).

    Switch

    A switch is used to control the flow of current in the circuit. When the switch is open, the circuit is incomplete, and current does not flow. When the switch is closed, the circuit is complete, and current flows.

    The simplest of electric circuit is made up battery and a conductor.

    showing simplest circuit in
    A very simple circuit made of a dry cell and a conductor

    This circuit above is simple and naive , to make a working circuit, you need to some few extra components.

    The bulb is used to show that current is flowing when the bulb lights. Opening the switch makes the bulb off showing that current off have been cut off. Current is conventionally set to flow opposite direction to the flow of charge.

    Convectional Circuit Diagram

    For clarity and neatness, symbols are used in representing components of an electric circuit. It would be tedious and clumsy to draw each of the components used in circuits. Therefore, we use symbols so that we can easily represent circuits in diagrams.

    The figure below shows the circuit that was shown above drawn in convectional ways using symbols.

    An open circuit

    On the diagram above, there is a gap on the switch. The loop from the positive terminal of the cell towards the negative one has a gap. The circuit is said to be incomplete or open. No current is flowing in such circuit and is usually referred as an open circuit.

    Switch acts like a gate, it connects two parts to make the circuit complete. When switch is closed, the circuit becomes complete. The figure below shows a complete circuit.

    table showing symbols used in simple electric circuit
    A closed circuit

    In the diagram below, current will flow from positive of the battery to the negative without encountering a gap. the bulb with thus light because it is in a closed circuit.

    While drawing or interpreting circuit diagrams, Connecting wires are drawn as straight lines with right angle corners. However, the actual wires are flexible and bent.

    The arrow-heads drawn on the lines indicates direction of the flow of current. Remember that, current flows opposite direction to that of charge flow.

    Short circuiting

    Short circuiting is a condition where an electric current is caused to flow through a path of low resistance to avoid the path with high resistance.

    Electric current usually follows a path of least resistance when moving.

    consider the figure below.

    simple electric circuit
    short circuiting a cell and a bulb

    Bulb is considered to be of much higher resistance compared to the conducting wire. In the above connection, current will flow through wire AB and avoid passing through the bulb. The bulb with thus not light and is said to be short circuited. In the figure above, both the cell and the bulb are short circuited.

    In the figure below only the bulb is short circuited.

    a short circuiting wire being connected across the bulb in a simple electric circuit
    short circuiting a bulb

    Common electrical symbols used in circuit diagrams

    each component in a circuit diagram has a unique symbol that represent it. The table below summarizes information about most of components used in circuit diagrams and their symbols.

    SymbolComponent name
    A cellcell
    battery symbol as used in simple circuitsbattery
    switch symbol used in simple circuit diagramswitch
    symbol for bulb used in simple circuitsbulb
    symbol for filament lampfilament lamp
    wires crossing without joining in simple circuitwires crossing without connecting
    Wires joining in a simple circuitwires crossing with connection
    Fixed resistor symbol used in circuit diagramsFixed resistor
    variable resistor symbol as used in simple circuit diagramsvariable resistor
    potential divider symbol used in circuit diagramspotential divider
    Rheostat symbol used in circuit diagramsrheostat
    capacitor symbol used in circuit diagramscapacitor
    fuse symbol in circuit diagramsfuse
    Ammeter symbol used in circuit diagramsAmmeter
    Voltmeter symbolvoltmeter
    Galvanometer symbolGalvanometer

    Related topics

  • Some applications of electromagnetic induction

    Some applications of electromagnetic induction

    Electromagnetic induction, the phenomenon where a changing magnetic field induces a voltage in a nearby conductor, has numerous practical applications. Some applications of electromagnetic induction include electric generators, transformers, induction cooking, and magnetic flow meters. 

    applications of electromagnetic induction: induction coil

    Induction coil is an important application of the electromagnetic induction. The induction coil consists of few turns of thick insulated copper wire wound on a primary coil. Then a secondary coil of many turns of thin insulated copper wire. we wound Both primary and secondary coil on a soft iron core. see the figure below:

    some applications of electromagnetic: induction coil

    The structure and working of the induction coil

    we connect the primary coil to a direct current source of low voltage. In the figure below , we have wound the primary and secondary coil on top of the other.

    The structure of the induction coil

    When we close the switch , the soft iron core becomes magnetised due to the current in the primary coil. This causes it to attract the soft iron armature. The moving armature armature opens the contacts and cuts off the primary current, rapidly reducing the magnetic field to zero. This induces a large a large e.m.f in the secondary coil by mutual induction. However, the spring pulls the armature back to its initial position. This action completes the circuit again in the primary circuit so that the current flow again. This process repeats itself.

    The switching on and off of the primary coil is thus continuous hence continuous changing magnetic flux. The induced e.m.f in the secondary coil is much higher when the primary coil is switching off than when switching it on. Remember the rate of current decay is usually higher than the rate of current build up in electromagnetic induction.

    Many secondary coil increases the magnitude of the induced e.m.f in the secondary coil.Spark then jumps across the gap G between the two ends of the secondary coil. Hence can be used to ignite petrol-air mixture in a car engine.

    Sparks may also occur at the contacts due to magnetic field of the primary coil. This cuts the primary coil fulfilling the Lenz’s law to keep primary current flowing.

    A capacitor connected across the contacts minimizes the sparking. This causes the primary current and hence the magnetic flux to decay smoothly to zero.

    some applications of electromagnetic induction: The moving-coil Microphone

    The moving-coil microphone is a popular application of the electromagnetic induction. A coil of wire is wound on a cylindrical former connected to a diaphragm and placed between the poles of a magnet. see the diagram below:

    some applications of electromagnetic: The moving-coil Microphone

    Sound waves from a source sets the diaphragm in vibration. Figure below shows a typical wave profile :

    moving-microphone wave profile

    This way, it causes the coil to move to and fro, cutting the magnetic field. The field is radial so that the motion is perpendicular to it for maximum flux linkage. An induced e.m.f of varying magnitude sets up varying current in the coil. An amplifier is used to increase the amplitude of this current before it is fed into a loudspeaker. In the loudspeaker, it is converted back to sound.

    Related topics

  • An Alternating current (a.c) generator

    An Alternating current (a.c) generator

    A generator is a device that converts mechanical energy into electrical energy. It works on the principle of electromagnetic induction, where a coil of wire rotates within a magnetic field, causing an electric current to be produced. The generated electricity is then transferred through slip rings and carbon brushes to an external circuit, where it can power electrical devices such as bulbs, motors, and appliances. Generators are widely used in power stations, industries, and homes as a source of electricity.

    An Alternating current (a.c) Generator is also refereed to as the alternator. An a.c generator is a device or machine that converts mechanical energy energy into electrical energy. It does this by rotating conductors through magnetic fields.

    Working of an a.c generator

    The figure below illustrates a simple generator. It is made of curved permanent rectangular magnetic poles, slip rings, a conductor made into a loop, and carbon brushes.

    illustrating the structure of an a.c generator

    The poles of magnets are curved so that the magnetic field is radial. Current enters and leaves the coil through the brushes which are pressing against the slip rings.

    Carbon brushes are preferred because they are good conductor, slippery to allow the wire slide along with ease and acts as a lubricant. The figure illustrates a.c generator more vividly.

    Illustrating an alternating current generator

    working of an a.c Generator

    The ac generator will produce electric current in the coil when the coil rotates through magnetic field using the principle of electromagnetic induction.

    When the coil rotates clockwise as indicated on the diagram at the rotation axis, edge AB rotates upwards. Meanwhile, edge CD rotates downwards. This causes the two edges to cut the magnetic field at right angles while in the horizontal position. The induced e.m.f is maximum when the coil is perpendicular to the magnetic field.

    Determining direction of current in a.c generator

    Using the Fleming’s right-hand rule, the flow of current is in direction A-B-C-D when the direction of rotation is clockwise. The induced current flows through the external circuit via the slip rings and through carbon brushes.

    As the coil rotates from a horizontal to a vertical position, the angle at which the sides of the coil cut the magnetic field decreases. It changes from 90o  to 0o. This causes the induced e.m.f to reduce from its maximum value (Eo) to zero e.m.f. when the coil becomes positioned vertically

    An overview of the cross-section of the coil in a magnetic field is shown below.

    wire rotating inside magnetic field in alternating current generator

    The coil rotates past the vertical position. At that moment, the sides AB and CD move parallel to the field. In that position, the coil does not cut the magnetic field. Therefore, the induced e.m.f is zero at that position.

    Past the vertical position, side AB and CD exchange position. Side AB starts moving downward while CD moves upward. The angle increases from 0o to 90o. This occurs as the sides of the coil cut the magnetic field and the coil returns to the horizontal position.

    When the angle is increasing from zero to 90o , the induced e.m.f increases from zero to maximum value Eo. When AB and CD exchange positions in the coil rotation, the direction of current flow reverses to D-C-B-A. This action makes brush y positive and makes brush x to be negative.

    As the coil rotates further to complete one revolution, its sides cut the magnetic field at a changing angle. This angle reduces from 90o to 0o. Consequently, the e.m.f induced in the coil reduces from maximum value Eo to zero.

    induction of e.m.f in the a.c generator

    The variation of the e.m.f increases from zero to maximum at one quarter cycle. Then it reduces from maximum to zero at the next quarter circle. Next, it starts increasing to maximum value in the negative direction in the third cycle. At the fourth cycle, it increases from maximum negative value to zero. Thus, in one complete oscillation of the coil, the variation of induced e.m.f against the angle of rotation forms a sinusoidal curve. The curve formed by this variation can be represented by the equation:

    E = Eo sin θ

    where E is an instantaneous e.m.f at any particular angle of rotation where Eo is the maximum e.m.f and θ the angle between plane of the coil and the vertical axis.

    The formation of the sine curve is as illustrated

    wave equation of an a.c generator

    By ohms law;

    $$I=\frac{E}{R}$$

    where R is the resistance of the circuit and I is an instantaneous current at random position of ration of the coil.

    $$Therefore, I = \frac{E_o}{R}sin\theta$$

    A typical graph of e.m.f against the angle θ is as illustrated

    After one complete circle, the rotation pattern repeats itself and many circles are made per unit time. The number of cycles made per second is referred as the frequency of the generator and is also the frequency of the a.c current.

    Most of generators used to make commercial power productions makes 50-60 revolutions per second. In USA, the frequency is 60Hz while in Europe and Asia, it is usually 50 Hz.

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  • Simple electric motor

    Simple electric motor

    Simple electric motor is a device that converts electrical energy into rotational kinetic energy. A Simple d.c motor consists of a coil of insulated wire between two poles of a magnet as shown in figure below.

    The coil ABCD can turn about a fixed axis within magnetic field provided by a strong curved permanent magnet. Electric current enters the coil through split ring P and then leaves the coil through split ring Q. We refers P and Q as the commutators.

    The two half rings are insulated from each other and brushes slightly press against the commutator . We then connect the brushes to the battery terminal.

    we are assuming that the original position of the coil is at the horizontal position before the current is switched. The current flows in the direction indicated on the diagram when switch is closed. Using Fleming’s left hand rule, side AB experiences an upward force while side CD experiences a downward force.

    Simple electric motor

    Since the magnitude of current on both sides is the same, the forces on the sides are equal but opposite. The forces therefore causes the coil rotate in clockwise until it reaches it’s vertical position with side AB up. In this position, the brushes touch the space between the two halves of the split rings cutting off the current flowing hence no force is acting on the sides AB and CD at this position.

    Simple Electric motor Coil: Rotation energy

    Due to the rotational kinetic energy, the momentum in the coil carries it past this vertical position and the two split rings exchange brushes. We reverse direction of the current through the coil and consequently direction of force on each side of the coil also changes. This process is referred as commutation.

    Side AB is now on the right hand side while CD is on the left hand side. Side AB experiences a downward force while CD experience an upward force.

    The coil ABCD will continue rotating in the clockwise so long as the current is flowing through it.

    If we increase current through the coil, the coil rotates at much high speed. The speed of rotation is thus proportional to the strength of current flowing.

    If someone inter-changes terminals of the battery, the direction of the current reverses. Consequently direction of rotation of the coil reverses to the opposite direction.

    How to make Simple electric Motor more effective

    We can make the D.C motor described above more powerful by adjusting its setup in several ways that include:

    • winding the coil on a soft iron core so that iron core becomes magnetized. This concentrates it’s magnetic field in the coil which greatly increases the force on the coil.
    • Increasing the number of turns of the rotating coil. This multiplies the force on the single coil by the number of turns made.
    • using a stronger magnet that provides more powerful magnetic fields.
    • Multiplying the number of coils and commutator segments.
    • Replacing the permanent magnet by an electromagnet. This way, we adjusts strength of the magnetic field as needed.

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    D. C motor

  • useful equations for transformers

    useful equations for transformers

    Useful equations for transformers relate voltage, current, and number of turns in the primary and secondary coils. In the equation, we assumes that the power we feed into the transformer is the same power given out. This assumption is based on another assumption that the coils of wire in the transformer is negligible.

    Electrical power = Current(I) x Voltage(V)

    power input from primary coil = Current in primary coil (Ip) x Voltage in primary coil(Vp)

    power output from secondary coil = Current in secondary(Is) x Voltage in secondary coil(Vs)

    For an ideal transformer that has no energy loss;

    Power input = power output

    that is: Ip x Vp = Is x Vs

    useful equations for transformers: The turn ratio

    From previous lessons, we learnt that the magnetic flux changes in the primary coil. This changing magnetic flux links with each turn in the secondary coil.

    transformer

    Total e.m.f in the secondary coil is the sum total of the e.m.f induced in each turn of wire in the secondary coil. The voltage produced in the secondary coil is proportional to the number of turns in that coil. The voltage changes as the number of turns changes. We show that, the secondary coil multiplies the voltage supplied from primary coil by a constant factor that is given by:

    $$\frac{\text{number of turns in secondary coil}(N_s)}{{\text{number of turns in primary coil}(N_p)}}$$

    From the above equation we can see that:

    $$\frac{\text{Secondary voltage}(V_s)}{\text{primary voltage}(V_p)} =\frac{\text{Number of turns in secondary voltage}(N_s)}{\text{Number of turns in primary voltage}(N_p)}$$

    in short form;

    $$\frac{(V_s)}{(V_p)} =\frac{(N_s)}{(N_p)}$$

    The above equation is know as the turns rule and helps determine voltage produced by a transformer.

    The useful equations for transformers

    From the equation :

    $$I_p \times \ V_p = I_s \ \times \ V_s$$

    we can obtain by rearranging the equation:

    $$\frac{I_p}{I_s} = \frac{V_s}{V_p}$$

    combining this with the turns rule equation we have:

    $$\frac{I_p}{I_s} = \frac{V_s}{V_p} = \frac{N_s}{N_p}$$

    Example 2 problems: useful equations for transformers

    A transformer is used to provide power to a 10 V lamp from an a.c mains supply of 240 V. What should be the number of turns of the secondary coil if primary coil has 1800 turns.

    solution to the problem

    This is a case of step-down transformer. The voltage from the mains needs to be reduced to 10 V needed by the lamp.

    $$\frac{V_s}{V_p} = \frac{N_s}{N_p}$$ $$hence$$ $$\frac{10}{240} = \frac{N_s}{1800}$$ $$\text{therefore:} N_s=\frac{10}{240} \ \times 1800 = 75 \ turns$$

    Example problem 2

    A power station has an output of 45KΩ at a potential difference of 10 Kv. A transformer with a primary coil of 2000 turns is used to step up the voltage to 140Kv for transmission. Assuming that there is no power losses in the transformer, calculate:

    (a) current in the primary coil

    (b) number of turns of the secondary coil

    (c) current in the secondary coil

    Example problem 3

    A power station has an output of 50Kw at a potential difference of 1000V. The voltage is stepped up to 30000Kv by transformer T1 for a transmission along a grid of resistance 2500 Ω and then stepped down to a voltage of 240V by transformer T2 at the end of grid for use in a home.

    (a) Given that the efficiency of T1 is 95% while that if T2 is 90%, find:

    (i) The power output of T1

    (ii) current in the grid

    (iii) Power loss in the grid

    (vi) input voltage of T2

    (v) the maximum power and current available for use in the home

    (b) Explain the purpose of stepping up the voltage at the power station

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  • Exam questions on current and electricity

    Exam questions on current and electricity

    Current and electricity are core topics in physics, encompassing electric current, circuits, resistance, and the behavior of electrons. Key areas that can be tested include the nature of electric current. Another key area is Ohm’s law, Series and parallel circuits, the heating effect of electric current among others

    Questions

    1. Figure 1 shows four identical bulbs connected to a 15 volt battery whose internal is negligible.
    Diagram for Exam questions on current and electricity. Question one
    Figure 1

    Determine the reading of the voltmeter V. (2 marks).

    2. Figure 14 shows a circuit in which a battery. a switch , a bulb, resistor P, a variable resistor Q. a voltmeter V and two ammeters A1 and A2 of negligible resistance are connected.

    P has a resistance of 10 Ω. When the switch is closed A1 and A2 reads 0.10 A and the voltmeter reads 1.5 V.

    (a) Determine;. 
          (i) the current passing through P;     (3 marks).

           (ii) the resistance of the bulb               (2 marks).

    (b) The variable resistor Q is now adjusted so that a larger current flows through A2 . 
     (i) State how this will affect the resistance of the bulb   (1 mark)


    (ii) Explain your answer in (b)(i).        (3 marks)


    (c) A house has one 100W bulb, two 60W bulbs and one 30W bulb. Determine the cost of having all the bulbs switched on for 70 hours,. given that the cost of electricity is 40 cents per kilowatt hour.    (3 marks).
    • 3. (a) Define current stating its S.I units.               (2 mark)
     (b) A battery circulates charges round a circuit for 1.5 minutes. If the current is held at 2.5 Amperes,   what quantity of charge passes though the wire? (2 marks)

    4. Figure 2 shows arrangement of three capacities of 10µF, 2µF and 5µF.

    network three capacities of 10µF, 2µF and 5µF and a cell of 2V

    Determine the effective capacitance. (3 marks)

    5.(a) Figure 8 shows a graph of potential difference V (volts) against a current I(amperes) for a certain device.

    From the graph:

    (i) State with a reason whether or not the device obeys ohms law.    (2 marks)

    (ii) determine the resistance of the device at ;

         (I) I =1.5 A           (2 marks)

          (II) I = 3.5 A         (2 marks)

    (iii) From the results obtained in (ii) state how the resistance of the device varies as the current increases.      ( 1 mark)

    (iv) State the cause of this variation in resistance.  (1 mark)

    5(b) Three identical dry cells each of e.m.f 1.6 V are connected in series to a resistor of  11.4 ohms.  A current of 0.32A flows in the circuit. Determine:

       (i) The total e.m.f of the cells     (1 mark)

      (ii) The internal resistance of each cell;    (3 marks)

    6. Figure 6 below shows an electric generator. The points P and Q are connected to a cathode ray oscilloscope (CRO).

    exam question on electric generator:
    Figure 6

    Sketch on the axes provided the graph of the voltage output as seen on the CRO, given that when t=0 the coil is at the position shown in the figure.   (2 marks).

    7. A 60 W bulb is used continuously for 36 hours. Determine the energy consumed. Give your answer in kilowatt hour (kWh).  (3 marks)

    8. Figure 8 shows the cross-section of a dry cell. Use the information on the figure to answer questions 4 and 5.

    Figure 8

    Name the parts labelled A and B. (2 marks)

    8 (b)  State the use of the manganese(IV) oxide in the cell. (1 mark).

    9. A 4 ohms resistor is connected in series to a battery of e.m.f 6.0 V and negligible internal . Determine the power dissipated by the resistor (2 marks)

    10. State the reason why electrical power is transmitted over long distances at very high voltages .(1 mark)

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