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Transformers and Power Transmission: Powering Our World
Discover the crucial role of transformers in power transmission systems. Learn how these devices enable efficient energy transfer across vast distances, ensuring reliable electricity distribution to homes and businesses.

Now Playing:Transformers and power transmission – Example 0a
Intros
  1. Introduction to transformers
  2. Transformers equations
Examples
  1. An ideal transformer with 120V, ac supply, on the primary coil supplies power to the resistor R. If this resistor dissipates 35W, what is the current in the primary coil and the secondary coil?

    Transformers and power transmission


    Transformers and power transmission
    Induced EMF and Lenz’s law
    Jump to:NotesConceptFAQsPrerequisites
    Notes

    In this lesson, we will learn:

    • What does a transformer do and what does it consist of?
    • Types of transformers
    • Transformers equations
    • How to reduce power loss in transmission lines?

    Notes:


    Transformers
    • A device for increasing or decreasing an ac voltage.
    • Example of transformers:

      1. There is a transformer in TV sets to provide high voltage for the picture tube.
      2. Utility poles require transformers to reduce the high voltage from the electric company to a useable voltage in houses.

    • Transformers operate only with ac voltages; dc voltage does not produce any change in flux to induce an emf.

    • A transformer consists of two coils, the primary coil, and a secondary coil.


    Transformers and power transmission


    • The two coils are interconnected with an iron core.
    • Nearly all magnetic flux produced in the primary coil is transferred to the secondary coil.
    • As the primary coil is connected to an ac voltage, the change in the magnetic field induced a current, which is then transferred to the secondary coil with the same frequency.
    • Due to the number of coils, the voltage would be different in the secondary coil compared to that of the primary.


    Transformers Equations


    According to Faraday’s law, the voltage induced in the secondary coil can be calculated using the following equation:

    Vs=NsV_{s} = N_{s} ΔϕBΔt\large \frac{\Delta \phi B} {\Delta t}


    Ns=N_{s} = number of turns in the secondary coil

    ΔϕBΔt=\large \frac{\Delta \phi B} {\Delta t} = the rate of change in flux

    The input voltage would be the result of the change in flux in the primary coil, therefore;

    Vp=NpV_{p} = N_{p} ΔϕBΔt\large \frac{\Delta \phi B} {\Delta t}


    Np=N_{p} = number of turns in the primary coil
    Assuming no or little amount of flux is lost, we divide the above two equations;

    VsVp=NsΔϕBΔtNpΔϕBΔt\large \frac{V_{s} } {V_{p} } = \frac{N_{s} \frac{\Delta \phi B} {\Delta t} } { N_{p} \frac{\Delta \phi B} {\Delta t} }  ⇒  \, \Rightarrow \, VsVp=NsNp \large \frac{V_{s}} {V_{p}} = \frac{N_{s}} {N_{p}} \, (transformer equation I )


    The above equation shows that the voltage in the secondary coil is related to the primary coil.


    Types of Transformers


    There are two types of transformer:

    1. Step-up transformer
      If the number of turns in the secondary coil is more than the primary coil; the voltage in the secondary coil would be higher than that of the primary.

      NsN_{s} > Np ⇒VsN_{p} \, \Rightarrow \quad V_{s} > VpV_{p}

    2. Step- down transformer
      If the number of turns in the primary coil is more than the secondary coil; the voltage in the primary coil would be higher than that of the secondary.

      NpN_{p} > Ns ⇒VpN_{s} \, \Rightarrow \quad V_{p} > VsV_{s}

    Note: the output power is equal to the input power in ideal transforms where their efficiency is 99%.

    P=IVP = IV

    Ps=IsVsP_{s} = I_{s} V_{s}

    Ps=Pp ⇒IsVs=IpVp⇒P_{s} = P_{p} \, \Rightarrow \quad I_{s} V_{s} = I_{p}V_{p} \quad \Rightarrow \quad IsIp=VpVs=NpNs \large \frac{I_{s}} {I_{p}} = \frac{V_{p}} {V_{s}} = \frac{N_{p}} {N_{s}}


    Pp=IpVpP_{p} = I_{p} V_{p}

    IsIp=NpNs  \large \frac{I_{s}} {I_{p}} = \frac{N_{p}} {N_{s}} \; (transformers equation II)



    Transmission Lines
    • Transformers are very important electric devices in transmitting electricity from the power plant to houses.
    • Since the power has to be transmitted over long distances, part of the energy will be lost in the transmission lines.
    • To minimize the loss in energy, the power is transmitted at high voltage.
    • This is done by
      • Using step-up transformers to increase the voltage, as the power leaves the power plant station.
      • Using step-down transformers to decrease the voltage before the power enters the houses.

    Example of Transmission Lines

    An average of 140 KW of electric power is sent from a power plant, 20 km away, to a small town. The total resistance of the transmission lines is 0.60Ω\Omega . calculate the power loss if the power is transmitted at:
    1. 240V
    2. 12000 V

    Solution
    • To find the power loss we should apply the equation P=I2RP = I^{2} R ,
    • The equation  P=V2R \, P = \frac{V^{2}} {R} \, does not work in this case, since we do not have the voltage drop across the lines.

    1. Step 1
      calculate the current:

      I=PV=1.4 × 1052.4 ×102=\large I = \frac{P} {V} = \frac{1.4 \, \times \, 10^{5}} {2.4 \, \times 10^{2}} = 583.3 AA

      Step 2
      Find the power loss:

      P=I2R=(583.3)2 (0.60)P = I^{2}R = (583.3)^{2} \, (0.60) = 204143.33 WW = 204KWKW

      Almost 60% of all overpower is lost in the power lines!!!!!

    2. If the transmission voltage increases to 12000VV,

      I=PV=1.4 × 1051.2 ×104=\large I = \frac{P} {V} = \frac{1.4 \, \times \, 10^{5}} {1.2 \, \times 10^{4}} = 11.6  A ≃\, A \, \simeq 12 AA

      P=I2R=\quad P = I^{2} R = (12)2(0.60) = 86.4WW

      the power loss decreases to 0.6%
    Concept

    Introduction to Transformers and Power Transmission

    Transformers play a crucial role in power transmission and electrical systems. The introduction video provides a comprehensive overview of these essential devices, offering valuable insights into their functionality and significance. Transformers are electromagnetic devices that transfer electrical energy between two or more circuits through electromagnetic induction. They are fundamental components in power distribution networks, enabling the efficient transmission of electricity over long distances. By stepping up or stepping down voltage levels, transformers ensure that power can be transmitted with minimal losses and distributed safely to end-users. In electrical systems, transformers serve various purposes, including voltage regulation, isolation, and impedance matching. Their ability to change voltage levels makes them indispensable in both residential and industrial applications. Understanding transformers is crucial for anyone involved in electrical engineering or interested in the intricacies of power transmission. The video introduction serves as an excellent starting point for grasping the basic principles and importance of transformers in modern electrical infrastructure.

    FAQs

    1. What is the transmission of power?

      Power transmission refers to the process of transferring electrical energy from power generation plants to substations near populated areas. This is typically done using high-voltage transmission lines to minimize power losses over long distances. Transformers play a crucial role in this process by stepping up the voltage for transmission and then stepping it down for distribution to end-users.

    2. What is a transformer and how does it work?

      A transformer is an electrical device that transfers energy between two circuits through electromagnetic induction. It consists of two or more coils of wire wound around a core, typically made of iron. When alternating current flows through the primary coil, it creates a changing magnetic field in the core, which induces a voltage in the secondary coil. The ratio of turns in the primary and secondary coils determines whether the transformer steps up or steps down the voltage.

    3. What are the 3 types of transformers?

      The three main types of transformers are:

      • Step-up transformers: Increase voltage for long-distance transmission
      • Step-down transformers: Decrease voltage for local distribution
      • Isolation transformers: Maintain the same voltage but provide electrical isolation between circuits

      Each type serves specific purposes in power systems and electrical applications.

    4. How do transformers work in the power grid?

      In the power grid, transformers are used at various stages:

      1. At power plants, step-up transformers increase voltage for efficient long-distance transmission.
      2. At substations, step-down transformers reduce voltage for regional distribution.
      3. On utility poles or in local areas, distribution transformers further reduce voltage for residential and commercial use.

      This system of transformers allows for efficient power transmission and safe distribution to end-users.

    5. How do transformers reduce transmission loss?

      Transformers reduce transmission loss by stepping up the voltage for long-distance transmission. Higher voltage means lower current for the same amount of power. Since power loss in transmission lines is proportional to the square of the current (I²R losses), reducing the current significantly decreases power loss. For example, transmitting power at 400 kV instead of 11 kV can reduce losses from over 20% to just 2-3% over the same distance.

    Prerequisites

    Understanding the fundamental concepts that lay the groundwork for more advanced topics is crucial in any field of study, and this is especially true when it comes to transformers and power transmission. While there are no specific prerequisite topics provided for this subject, it's important to recognize that a strong foundation in basic electrical principles and physics is essential for grasping the complexities of transformers and power transmission systems.

    To fully comprehend transformers and power transmission, students should have a solid understanding of electrical circuits, magnetism, and electromagnetic induction. These foundational concepts form the basis for how transformers function and how electrical power is transmitted over long distances. Without this knowledge, it can be challenging to grasp the intricacies of transformer design, operation, and their role in power distribution networks.

    Additionally, a basic understanding of alternating current (AC) and direct current (DC) is crucial. Transformers primarily work with AC power, and understanding the characteristics of AC circuits is vital for comprehending how transformers step voltage up or down. This knowledge also helps in understanding why AC is preferred for long-distance power transmission over DC.

    Mathematics, particularly trigonometry and complex numbers, plays a significant role in analyzing transformer behavior and power transmission systems. These mathematical tools are essential for calculating power factors, phase angles, and other important parameters in electrical systems.

    Furthermore, a basic grasp of materials science can be beneficial, as it helps in understanding the properties of core materials used in transformers and the conductors used in power transmission lines. This knowledge aids in comprehending efficiency considerations and loss reduction techniques in both transformers and transmission systems.

    While not explicitly listed as prerequisites, familiarity with electrical safety principles is also crucial when studying transformers and power transmission. These systems deal with high voltages and currents, and understanding the associated risks and safety measures is paramount for anyone working in this field.

    By building a strong foundation in these related areas, students will find themselves better equipped to tackle the complexities of transformers and power transmission systems. This comprehensive understanding not only facilitates easier learning of advanced concepts but also enables a deeper appreciation of the intricate workings of our modern electrical infrastructure.

    In conclusion, while specific prerequisites may not be listed, the importance of a well-rounded understanding of electrical fundamentals cannot be overstated when approaching the study of transformers and power transmission. This knowledge serves as the building blocks for more advanced concepts and ensures a more thorough and meaningful learning experience in this critical area of electrical engineering.