15.6 Transformers
3 min read•june 24, 2024
Transformers are the unsung heroes of our electrical grid. They enable efficient over long distances by manipulating voltage and current. Without them, we'd struggle to deliver electricity safely and economically to our homes and businesses.
At their core, transformers rely on a simple principle: the ratio of turns in their windings determines voltage and current changes. This allows them to step up voltage for transmission and step it down for consumer use, all while maintaining power balance.
Transformers
Transformers for long-distance power transmission
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- Enable efficient transmission of electrical power over long distances by stepping up voltage and stepping down current
- High voltage (typically hundreds of ) and low current minimize power losses due to resistance in ()
- Reduces the amount of power dissipated as heat in the
- Allows for the use of thinner, less expensive wires for transmission
- High voltage (typically hundreds of ) and low current minimize power losses due to resistance in ()
- At the receiving end, transformers step down the voltage and step up the current to levels suitable for safe use by consumers
- Common consumer voltages are 120V and 240V (United States)
- Ensures that the power delivered to homes and businesses is at a safe and usable level
Voltage and current in transformers
- Voltage ratio between primary and secondary windings equals the 's
- , where and are primary and secondary voltages, and and are the number of turns in primary and secondary windings
- Example: A with 1000 primary turns and 100 secondary turns has a turns ratio of 10:1, so the secondary voltage is 1/10th of the primary voltage
- Current ratio is inversely proportional to the turns ratio
- , where and are primary and secondary currents
- In the previous example, the secondary current would be 10 times the primary current
- Step-up transformers have higher secondary voltage and lower secondary current compared to primary
- Step-down transformers have lower secondary voltage and higher secondary current compared to primary
Primary vs secondary windings in transformers
- In an ideal transformer, power input to primary winding equals power output from secondary winding
- , where is primary power and is secondary power
- Relationship expressed as
- Real transformers have efficiency slightly below 100% due to losses
- Copper losses in windings from resistance
- Iron losses in core from and
- Power transfer depends on between primary and secondary windings
- Determined by number of turns in each winding, core cross-sectional area, and core material's
- Higher mutual inductance results in more efficient power transfer between windings
- Achieved through careful design of core geometry and material selection ()
- Proper winding techniques to minimize and
Transformer Applications and Principles
- Transformers operate on systems, utilizing electromagnetic induction
- Essential for power transmission over long distances, minimizing energy losses
- Used for in electronic circuits, optimizing power transfer between components
- Magnetic permeability of the core material affects the transformer's efficiency and performance
Key Terms to Review (35)
Alternating Current (AC): Alternating current (AC) is an electric current that periodically reverses direction, in contrast to direct current (DC) which flows in a constant direction. AC is the standard form of electricity supplied to homes and businesses, and it is the primary type of current used in power transmission and distribution systems.
B-field: The B-field, also known as the magnetic field, is a vector field that describes the magnetic influence exerted by electric currents and magnetic materials. It is a fundamental concept in electromagnetism and is crucial for understanding the behavior of charged particles and the operation of various electrical devices.
Eddy Currents: Eddy currents are circular electric currents that are induced within a conductive material when it is exposed to a changing magnetic field. These currents flow in a direction that opposes the changes in the magnetic field, creating their own opposing magnetic field.
Faraday's law: Faraday's law states that a change in magnetic flux through a circuit induces an electromotive force (emf) in that circuit. This principle is crucial for understanding how magnetic fields interact with electric circuits and lays the foundation for many applications in electromagnetism.
Ferromagnetic core: A ferromagnetic core is a material, typically made of iron or a similar ferromagnetic substance, that significantly enhances the magnetic field within it when exposed to an external magnetic field. This core is crucial for improving the efficiency of electromagnetic devices by concentrating and amplifying the magnetic field, which in turn influences energy storage and transfer in magnetic systems and is vital for the operation of transformers.
Flux linkage: Flux linkage is a measure of the total magnetic flux that passes through a coil of wire, multiplied by the number of turns in the coil. It represents how much magnetic field is linked with the coil and is crucial in understanding how changes in magnetic fields can induce electromotive force (EMF) in circuits. This concept plays a central role in understanding electromagnetic induction and its applications, highlighting how electricity can be generated from magnetic fields.
Hysteresis: Hysteresis is the lag between an input and output in a system, often observed in magnetic materials where the magnetization lags behind the applied magnetic field. This phenomenon results in a looped curve when plotting magnetization against the magnetic field strength.
Hysteresis: Hysteresis is a phenomenon where the response of a system depends on its past history and experiences. It describes the lagging of an effect behind its cause, or the inability of a system to return to its original state when the forces acting on it are removed.
Impedance Matching: Impedance matching is the practice of designing the input or output of an electrical device, such as an amplifier, filter, or transmission line, to maximize the power transfer or minimize signal reflection from the load. It is a crucial concept in the design and operation of various electronic systems.
Kilovolts: Kilovolts (kV) is a unit of electrical potential or voltage, where one kilovolt is equal to one thousand volts. It is commonly used to measure the high voltages found in electrical power transmission and distribution systems, as well as in certain scientific and medical equipment.
Laminated Silicon Steel: Laminated silicon steel, also known as electrical steel or transformer steel, is a specialized alloy material used in the core of electrical transformers. It is composed of thin, insulated steel sheets that are stacked and laminated together to form the transformer core, which is responsible for efficiently transforming and transferring electrical energy between circuits.
Leakage Inductance: Leakage inductance is a type of inductance that occurs in transformers due to the imperfect coupling between the primary and secondary windings. It represents the magnetic flux that does not link both windings, resulting in energy losses and reduced transformer efficiency.
Lenz's Law: Lenz's law is a fundamental principle in electromagnetic induction that describes the direction of the induced current in a conductor. It states that the direction of the induced current will be such that it opposes the change in the magnetic field that caused it, in accordance with Faraday's law of electromagnetic induction.
Magnetic Permeability: Magnetic permeability is a measure of the ability of a material to support the formation of a magnetic field within itself. It describes the degree of magnetization of a material in response to an applied magnetic field, and is a fundamental property that determines the strength and behavior of magnetic fields within a material.
Mutual Inductance: Mutual inductance is a measure of the magnetic coupling between two electrical circuits or coils. It describes the amount of induced voltage in one circuit due to a changing current in another circuit, and it is a key concept in understanding the principles of electromagnetic induction.
Mutual inductance (M): Mutual inductance is the phenomenon where a change in current in one coil induces an electromotive force (EMF) in a nearby coil. It is quantified by the mutual inductance coefficient, $M$, which depends on the geometry and orientation of the coils.
Nikola Tesla: Nikola Tesla was a Serbian-American inventor, electrical engineer, and futurist best known for his contributions to the design of the modern alternating current (AC) electricity supply system. His work on electromagnetic induction and transformers had a profound impact on the applications of electromagnetic induction and the development of power distribution systems.
Power Transmission: Power transmission refers to the process of transferring electrical or mechanical power from one point to another, often over long distances. It is a crucial component in the context of transformers, as transformers play a vital role in efficiently transmitting power across electrical systems.
Primary Coil: The primary coil is a fundamental component in the operation of transformers, where it acts as the input winding that receives the alternating current (AC) from the power source. It is responsible for generating a varying magnetic field that induces a voltage in the secondary coil, enabling the transformation of electrical energy between the two coils.
Secondary Coil: The secondary coil is a component in a transformer that receives the induced current from the primary coil. It is responsible for transforming the voltage and current levels between the input and output of the transformer.
Step-down transformer: A step-down transformer is a device that reduces the voltage from the primary winding to the secondary winding while increasing the current. It operates on the principle of electromagnetic induction and follows the transformer equation.
Step-Down Transformer: A step-down transformer is an electrical device that reduces the voltage of an alternating current (AC) power supply. It is commonly used to convert a higher voltage to a lower voltage, making it suitable for powering various electronic devices and appliances that require a lower voltage input.
Step-up transformer: A step-up transformer increases the voltage from the primary coil to the secondary coil while decreasing the current. It is commonly used in power transmission to reduce energy loss over long distances.
Step-up Transformer: A step-up transformer is an electrical device that increases the voltage of an alternating current (AC) by transforming it from a lower to a higher voltage level. It is a type of transformer that is widely used in power transmission and distribution systems to efficiently transfer electrical energy over long distances.
Stray Capacitance: Stray capacitance, also known as parasitic capacitance, is an unintended and unwanted capacitance that can occur in electronic circuits. It arises from the physical proximity and arrangement of circuit components, conductors, and dielectric materials, which can lead to the formation of capacitive couplings between different parts of the circuit.
Tesla: The tesla (T) is the SI unit of magnetic flux density, representing the strength of a magnetic field. One tesla is defined as one weber per square meter.
Tesla: The tesla (T) is the unit of magnetic flux density, or magnetic field strength, in the International System of Units (SI). It is named after the Serbian-American inventor Nikola Tesla, who made significant contributions to the field of electromagnetism. The tesla is a fundamental unit that is essential in understanding and describing various electromagnetic phenomena and their applications.
Transformer: A transformer is an electrical device that transfers electrical energy between two or more circuits through electromagnetic induction. It can change the voltage level of alternating current (AC) in a circuit.
Transformer: A transformer is a device that uses electromagnetic induction to transfer electrical energy from one circuit to another, usually to change the voltage or current levels between the two circuits. It is a fundamental component in various applications of electricity and electronics.
Transformer equation: The transformer equation describes the relationship between the primary and secondary windings of a transformer. It relates the voltages and number of turns in each winding: $\frac{V_s}{V_p} = \frac{N_s}{N_p}$, where $V$ represents voltage and $N$ represents the number of turns.
Transmission lines: Transmission lines are specialized cables or other structures designed to conduct alternating current (AC) and radio frequency (RF) signals from one point to another with minimal loss. They are essential in the efficient transfer of electrical energy over long distances.
Transmission Lines: Transmission lines are electrical conductors used to transport electrical energy over long distances. They are an essential component in power distribution systems, connecting power generation sources to end-users, and play a crucial role in the context of transformers.
Turns Ratio: The turns ratio is a fundamental characteristic of a transformer that describes the ratio of the number of turns in the primary winding to the number of turns in the secondary winding. This ratio is a critical factor in determining the voltage transformation capabilities of a transformer.
Weber: The weber (Wb) is the SI unit of magnetic flux, representing the quantity of magnetism. One weber is equal to one tesla meter squared ($1 \, \text{Wb} = 1 \, \text{T} \cdot m^2$).
Weber: The weber (symbol: Wb) is the unit of magnetic flux in the International System of Units (SI). It is named after the German physicist Wilhelm Eduard Weber. The weber is a fundamental unit that is closely related to the concepts of magnetic field, electromagnetic induction, and the functioning of various electrical and electronic devices.