Name: delta-wye network conversion
Uploaded: 2025-05-22T09:06:14.000Z
Duration: 1 min 16 s
Channel: JoVE

K12 Standards

Arizona Science Standards

High School

Physical Science

HS+Phy.P4

HS+Phy.P4U1.8

Equivalent Resistance

تستخدم التطبيقات العملية ، مثل ناقل الحركة والمحركات الكهربائية ثلاثية الطور ، شبكات Y أو T ثلاثية الأطراف القابلة للتحويل ، وشبكات دلتا أو pi.
ضع في اعتبارك شبكة دلتا مكونة من ثلاثة مقاومات. يتضمن تحويلها إلى شبكة Y تراكب شبكة Y المقابلة على شبكة دلتا عن طريق إضافة عقدة مركزية.
نظرا لأن المقاومة بين كل زوج من العقد في شبكة دلتا تعادل المقاومة بين نفس الزوج في شبكة Y ، يتم إنشاء مجموعة من ثلاث معادلات. ينتج عن حل هذه المعادلات مقاومات الشبكة Y.
في الشبكة Y ، قيمة كل مقاوم هي نتاج المقاومات في فرعي دلتا المتجاورين ، مقسومة على مجموع مقاومات دلتا الثلاثة.
وبالمثل ، يمكن تحويل شبكة Y إلى شبكة دلتا مكافئة. في شبكة دلتا ، يتم تحديد قيمة كل مقاوم عن طريق جمع جميع المنتجات الممكنة لمقاومات Y التي تؤخذ اثنين في كل مرة ثم القسمة على المقاوم Y المعاكس.
بالنسبة لشبكة متوازنة ذات مقاومات متساوية في كل من تكوينات Y و delta ، يتم تبسيط صيغة التحويل.

شبكات دلتا وواي

<div style="direction:rtl">في تحليل الدوائر، غالبًا ما تنشأ مواقف حيث لا تكون المقاومات على التوالي ولا على التوازي. لمعالجة مثل هذه السيناريوهات، يتم تشغيل شبكات مكافئة ثلاثية الأطراف مثل شبكات واي (Y) (الشكل 1 (أ) أو Tee (T) وشبكة دالتا (Δ) (الشكل 1 )(b) أو شبكات pi (π). توفر هذه الشبكات حلولاً متعددة الاستخدامات ويتم استخدامها بشكل متكرر في تطبيقات مختلفة، بما في ذلك الأنظمة الكهربائية ثلاثية الطور، والمرشحات الكهربائية، والشبكات المطابقة. <img alt="Figure1" src="/files/ftp_upload/15074/15074_PT_Figure_1.svg" style="text-align: center; height: 160px;"> ويكمن جوهر هذه الشبكات في قدرتها على التكيف. يمكن استخدامها بشكل فردي أو دمجها في دوائر أكثر تعقيدًا. على سبيل المثال، عند التعامل مع شبكة دلتا ولكن تجد أنه أكثر ملاءمة للعمل مع شبكة واي، يمكن فرض شبكة واي على تكوين دلتا الحالي. لتحديد المقاومة المكافئة داخل شبكة واي، يعد التأكد من أن المقاومة بين كل زوج من العقد في شبكة الدلتا تساوي المقاومة بين نفس زوج العقد في شبكة Y أو ( T) أمرًا بالغ الأهمية. تتضمن عملية التحويل بين هذه الشبكات علاقات رياضية تتعلق بالمقاومات. يتم تسهيل التحويل من خلال إدخال عقدة إضافية 'n' والالتزام بقاعدة التحويل: في شبكة Y، كل مقاوم هو نتاج المقاومات في فرعي Δ )دلتا( المتجاورين، مقسومًا على مجموع الثلاثة Δ المقاومات. على العكس من ذلك، لتحويل شبكة واي إلى شبكة دلتا مكافئة، يمكن للمرء استخدام قاعدة التحويل التالية: كل مقاوم في الشبكة هو مجموع جميع المنتجات الممكنة لمقاومات Y مأخوذة من اثنين في المرة الواحدة، مقسومًا على المقاوم Y المعاكس. يتم تبسيط صيغ التحويل هذه للشبكات المتوازنة حيث تكون المقاومات في التكوينين Y وΔ متساوية. لا يتضمن هذا التحويل إضافة أو إزالة مكونات من الدائرة ولكنه يستبدل أنماط شبكة ثلاثية الأطراف مكافئة رياضيًا. إنه يحول الدائرة بشكل فعال، مما يسمح بتحليل المقاومات كما لو كانت إما متصلة على التوالي أو متوازية، مما يسهل حساب المقاومة المكافئة إذا لزم الأمر.</div>

تستخدم التطبيقات العملية ، مثل ناقل الحركة والمحركات الكهربائية ثلاثية الطور ، شبكات Y أو T ثلاثية الأطراف القابلة للتحويل ، وشبكات دلتا أو pi.
...

Education

JoVE Core

Electrical Engineering

الهندسة الكهربائية

Unit 1

الوحدة الأولى

Basics of Electric Circuits

أساسيات الدوائر الكهربائية

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

delta-wye network conversion

Delta-wye network conversion helps analyze resistor circuits that are not arranged in simple series or parallel paths. These three-terminal equivalent networks use the wye (Y), also called tee (T), and the delta (Δ), also called pi (π), as practical circuit models.

These networks are useful in many circuit settings. They appear in three-phase electrical systems, electrical filters, and matching networks. They can also be used on their own or combined with more complex circuits.

A delta network can be replaced with an equivalent wye network when that makes the circuit easier to solve. The key rule is that the resistance between each pair of nodes must stay the same in both networks. To find the wye resistors, each one is the product of the two adjacent delta resistors divided by the sum of all three delta resistors.

A wye network can also be converted into an equivalent delta network. In this case, each delta resistor is found from the sum of all possible pairs of wye-resistor products, divided by the opposite wye resistor. These formulas become simpler for balanced networks, where the resistances in the Y and Δ forms are equal. The transformation does not add or remove parts from the circuit. It replaces one mathematically equivalent three-terminal pattern with another, which can make later equivalent-resistance calculations easier.

Delta-Wye Network Conversion

charge and current

Electric Charge in Circuits

Electric charge in circuits explains how charged particles behave in matter and how current is produced. Everyday static effects, like a wool sweater sticking to the body or a shock from a carpet, show charge in action. Charge is an inherent property of atomic particles and is measured in coulombs (C). Matter is made of atoms with electrons, protons, and neutrons. Electrons carry a negative charge (-e), and protons carry a positive charge (+e). These two charges have the same magnitude. An...

voltage

Voltage in Electric Circuits

Voltage in electric circuits is the energy needed to move electric charge between two points. It is also called electromotive force, or EMF. In most circuits, an external force such as a battery provides this energy for electron movement in a conductor. The voltage between points a and b is written as v_ab. It is defined as the work, or energy, needed to move a unit charge from point a to point b. In the equation, w is the energy in joules and q is the charge in coulombs. Voltage is measured...

power and energy

Circuit Power, Absorption, and Supply

Circuit power, absorption, and supply explain how much energy an element uses or delivers in an electric circuit. These ideas matter in electrical engineering because power and energy calculations help describe circuit behavior. A 100-watt light bulb, for example, emits more light than a 60-watt bulb, so wattage is a useful measure in real devices. Power is the time rate of expending or absorbing energy. It is measured in watts, written as W. The relation between power and energy uses the...

electric circuit elements

Circuit Elements: Passive, Active, and Linear

Circuit elements are the building blocks of an electric circuit. An electric circuit is the connection of these elements. In this context, circuit elements are often grouped by how they behave and whether they supply energy. One major group is passive elements. These elements do not generate energy. Common passive elements include resistors, capacitors, and inductors. The other group is active elements, which can generate energy. Generators, batteries, and operational amplifiers are typical...

circuit terminology

Circuit Parts: Branches, Nodes, and Loops

Circuit parts like branches, nodes, loops, and meshes help describe how electrical networks work. An electrical network is a system of connected elements, such as resistors, capacitors, inductors, and voltage or current sources. Unlike a circuit, a network does not have to form a closed path. A circuit is also made of connected electrical elements, but it must include one or more closed paths. These loops let current flow continuously, which is what makes the circuit operate. Because of this,...

independent and dependent sources

Circuit Source Symbols and Controls

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ohm's law

Resistance and Conductance in Circuits

Resistance and conductance help explain how electric current moves through a circuit. Resistors are basic circuit parts made from metallic alloys or carbon compounds. They are used to model how a material resists current and to control and regulate electrical power in a circuit. Ohm's law describes the link between voltage and current across a resistor. The voltage across a resistor is directly proportional to the current through it. The constant that sets this relationship is resistance.

kirchhoff's current law

Kirchhoff's Current Law at Circuit Nodes

Kirchhoff's Current Law explains how current behaves at a circuit node. A node is the point where two or more circuit elements meet. The law says the current entering a node equals the current leaving it. That balance follows the rule of charge conservation, which means electric charge is not lost at the junction. When applying KCL, currents entering the node are treated as positive and currents leaving the node are treated as negative. The currents can be added algebraically at the node, and...

kirchhoff's voltage law

Voltage Balance in Closed Circuit Loops

Kirchhoff's Voltage Law explains how voltage is balanced in a closed circuit loop. It is a basic rule in electrical engineering and comes from the idea of energy conservation. Energy can change form, but it cannot be created or destroyed. KVL states that the algebraic sum of all voltages around a closed path, or loop, is zero. In other words, the total voltage supplied in a loop equals the total voltage drop across the components in that loop. A loop can be traced clockwise or anticlockwise,...

voltage dividers

Series Resistors and Voltage Split

Series resistors split voltage across a circuit. In a series setup, resistors are linked one after another. The same current flows through each resistor in the chain. To analyze this behavior, Ohm's law is used to relate voltage, current, and resistance. Kirchhoff's voltage law says the voltages around a series loop add up to the source voltage. That means the current in the circuit equals the source voltage divided by the total resistance in series. The current value can then be used in Ohm's...

current dividers

Parallel Resistors and Current Division

Parallel resistors share the same two nodes, so each resistor has the same voltage across it. In this circuit setup, Kirchhoff's current law applies. The source current equals the sum of the currents through each branch. Ohm's law helps find the branch currents from the source voltage and the resistor values. The source current is equal to the source voltage times the sum of the reciprocals of the resistances. This makes it easier to calculate how current divides in the circuit. The current...

equivalent resistance

Delta-wye network conversion helps analyze resistor circuits that are not arranged in simple series or parallel paths. These three-terminal equivalent networks use the wye (Y), also called tee (T), and the delta (Δ), also called pi (π), as practical circuit models. These networks are useful in many circuit settings. They appear in three-phase electrical systems, electrical filters, and matching networks. They can also be used on their own or combined with more complex circuits. A delta...

design example: resistive touchscreen

Resistive Touchscreen Voltage Mapping

A resistive touchscreen uses voltage mapping to locate a finger touch on a mobile device. It is built from two metallic layers. The top layer is flexible, and the bottom layer is rigid. A narrow gap separates them, and the high resistance between the layers is an important part of the design. When a user touches the screen, the two layers meet at one point. That contact point is called the touchpoint. The touch lowers the resistance between the layers at that spot and changes the electrical...

key terms and concepts

Learn how delta and wye resistor networks are converted into equivalent forms to simplify circuit analysis when resistors are not in series or parallel.

Delta-Wye Network Conversion | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

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Delta-Wye Network Conversion

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