Name: current sources in mesh circuit analysis
Uploaded: 2024-04-11T12:48:30.000Z
Duration: 1 min 10 s
Channel: JoVE

يعد تحليل الشبكة أبسط في الدوائر ذات المصادر الحالية لأنها تتطلب معادلات أقل للتحليل.
ضع في اعتبارك دائرة ذات شبكتين مع مصدر تيار في شبكة واحدة فقط.
يتم تعيين تيارات الشبكة ، ويتم استبعاد الفرع الذي يحتوي على المصدر الحالي من تحليل الشبكة.
يتم تطبيق قانون جهد كيرشوف على الشبكة المتبقية للحصول على معادلة خطية.
نظرا لأن التيار في الشبكة الثانية متساوي في الحجم ولكنه معاكس في الاتجاه لتيار المصدر ، فإن المعادلة المبسطة تسمح بتحديد التيار في الشبكة الأولى.
الآن ، ضع في اعتبارك دائرة أخرى ذات مصدر حالي بين كلتا الشبكتين.
يتم إنشاء شبكة فائقة أكبر عن طريق استبعاد المصدر الحالي والعناصر المتصلة به في سلسلة.
مرة أخرى ، يؤدي تطبيق قانون جهد كيرشوف على الشبكة الفائقة إلى معادلة خطية.
بالإضافة إلى ذلك ، يتم تطبيق قانون كيرشوف الحالي على عقدة حيث يتم توصيل الفرع بالمصدر الحالي ، مما ينتج عنه معادلة خطية أخرى تربط التيارين الفرعيين.
توفر حلول المعادلات المتزامنة قيم التيارات الشبكية.

التحليل الشبكي للدوائر التي تحتوي على مصادر للتيار

<div style="direction:rtl">يصبح التحليل الشبكي أكثر بساطة عند تحليل الدوائر التي تحتوي على مصادر تيار، سواء كانت هذه المصادر مستقلة أو غير مستقلة. إذ تساهم مصادر التيار في تقليل عدد المعادلات اللازمة للتحليل. ويمكن توضيح ذلك من خلال حالتين رئيسيتين: تواجد مصدر التيار في شبكة واحدة: تتم عملية التحليل بطريقة مباشرة عندما يوجد مصدر تيار في شبكة واحدة فقط داخل الدائرة. يتم تعيين تيارات الشبكة كالمعتاد، مع استبعاد الشبكة التي تحتوي على مصدر التيار من عملية التحليل. يتم تطبيق قانون كيرشوف للجهد على الشبكات المتبقية، مما يؤدي إلى الحصول على معادلة خطية. ونظرًا لأن التيار في الشبكة التي تحتوي على المصدر يكون مساوياً في المقدار ولكنه معاكس في الاتجاه، فإنه يمكن بسهولة تحديد قيمة التيار في الشبكة الأولى. تواجد مصدر التيار بين شبكتين: في الحالات التي يكون فيها مصدر التيار واقعًا بين شبكتين، يمكن تبسيط التحليل من خلال إنشاء شبكة فائقة . يتم ذلك عن طريق استبعاد مصدر التيار وأي عناصر متصلة به على التوالي. بعد ذلك، يتم تطبيق قانون كيرشوف للجهد على الشبكة الفائقة، مما يؤدي إلى الحصول على معادلة خطية. بالإضافة إلى ذلك، يُطبق قانون كيرشوف للتيا ر عند العقدة التي يتصل بها الفرع المحتوي على مصدر التيار، مما يؤدي إلى معادلة خطية إضافية تربط بين التيارين الفرعيين. من خلال حل هذه المعادلات، يمكن تحديد قيم تيارات الشبكة بدقة. الخصائص الأساسية للشبكة الفائقة : <ul style="padding-right: 35px; list-style-type: disc;"> <li style="text-align: right;">يمكن استخدام مصدر التيار المتواجد داخل الشبكة الفائقة في استنباط معادلة خطية لحل تيارات الشبكة.</li> <li style="text-align: right;">لا تمتلك الشبكة الفائقة تيارًا خاصًا بها، وإنما تشتمل على التيارات الخاصة بالشبكات الفردية التي تكونها</li> <li style="text-align: right;">يتم تطبيق قانون كيرشوف للجهد وقانون كيرشوف للتيار على الشبكة الفائقة بنفس الطريقة التي يتم بها تطبيقهما على أي شبكة أخرى.</li> </ul></div>

يعد تحليل الشبكة أبسط في الدوائر ذات المصادر الحالية لأنها تتطلب معادلات أقل للتحليل.
ضع في اعتبارك دائرة من شبكتين بتيار ...

Education

JoVE Core

Electrical Engineering

الهندسة الكهربائية

Unit 1

الوحدة الأولى

DC Circuit Analysis

تحليل دوائر التيار المستمر

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

Mesh Analysis with Current Sources

current sources in mesh circuit analysis

Current sources make mesh circuit analysis easier because they can reduce the number of equations needed. This applies to both independent and dependent current sources. The method depends on where the current source is placed in the circuit.

When a current source appears in only one mesh, the setup is simple. Assign mesh currents as usual, but leave out the mesh that contains the current source from the equation process. Then apply Kirchhoff's voltage law, or KVL, to the remaining mesh to get a linear equation. The current in the mesh with the source is equal in magnitude but opposite in direction, so the first mesh current is easy to find.

A different case happens when a current source lies between two meshes. Here, the circuit can be handled with a supermesh, which is formed by excluding the current source and any elements in series with it. KVL is applied around the supermesh to create a linear equation. Then Kirchhoff's current law, or KCL, is used at a node connected to the current-source branch to link the two branch currents.

The current source inside a supermesh adds a needed constraint equation for solving the mesh currents. A supermesh has no current of its own. It combines the currents from the meshes it encloses. KVL and KCL are still applied to the supermesh like they are in any other mesh.

Current Sources in Mesh Circuit Analysis

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Supernode Equations in Nodal Analysis

Nodal analysis uses node voltages and Kirchhoff’s laws to solve circuits with voltage sources. It is a systematic method for breaking a complex circuit into smaller parts that are easier to analyze. In this example, the circuit includes four resistors and two voltage sources. One voltage source is connected between a non-reference node and the reference node. In that case, the non-reference node voltage can be written directly as the source voltage. This removes one unknown and makes the...

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Mesh Currents for Circuit Analysis

Mesh currents give students a simpler way to analyze planar circuits. In mesh analysis, the unknowns are currents, not voltages. The method uses Kirchhoff's voltage law, or KVL, to build the equations needed to solve the circuit. A mesh is a closed loop in a circuit that does not contain any smaller loops inside it. Each independent mesh is assigned a mesh current, and this current is usually drawn in the clockwise direction. These mesh currents are used as the main circuit variables during...

mesh analysis with current sources

Current sources make mesh circuit analysis easier because they can reduce the number of equations needed. This applies to both independent and dependent current sources. The method depends on where the current source is placed in the circuit. When a current source appears in only one mesh, the setup is simple. Assign mesh currents as usual, but leave out the mesh that contains the current source from the equation process. Then apply Kirchhoff's voltage law, or KVL, to the remaining mesh to get...

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Circuit Source Equivalents

Circuit source equivalents make it easier to simplify electrical circuits in circuit analysis. A source transformation replaces a voltage source in series with a resistor by a current source in parallel with a resistor, or it replaces a current source in parallel with a resistor by a voltage source in series with a resistor. The key idea is that the equivalent resistance at the circuit terminals stays the same when the original sources are turned off. When making the change, the current source...

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Circuit Linearity and Resistor Behavior

Circuit linearity describes how a circuit responds when its input changes. A linear circuit has an output that is directly proportional to its input. This behavior follows two rules: homogeneity and additivity. Homogeneity means that if the input, or excitation, is multiplied by a constant factor, the response is multiplied by the same factor. For example, if the current is increased by a constant k, the voltage also increases by k times. Additivity means that the response to a sum of inputs...

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Analyzing Circuits with Superposition

Superposition is a circuit analysis method for linear circuits with more than one independent source. It lets you find the voltage across or current through an element by adding the separate effects of each source acting alone. To use superposition, keep one independent source active and turn off the others. A voltage source is replaced by a short circuit, and a current source is replaced by an open circuit. Then calculate the output from the single active source. Repeat the process for each...

thevinin's theorem

Thevenin Circuit Equivalents

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norton's theorem

Norton Equivalent Circuit in DC Analysis

Norton equivalent circuit in DC analysis shows how a linear two-terminal circuit can be replaced by a simpler network. The replacement uses a current source, called I_N, in parallel with a resistor, called R_N. I_N is the short-circuit current through the terminals, and R_N is the input or equivalent resistance seen at the terminals when the independent sources are turned off. To find Norton's resistance, all independent sources in the circuit are set to zero. The resistance measured at the...

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Load Matching in Thevenin Circuits

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key terms and concepts

Learn how current sources simplify mesh circuit analysis, including one-mesh cases and supermeshes, using KVL and KCL to solve for mesh currents.

Current Sources in Mesh Circuit Analysis | 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.

electrical engineering

Current Sources in Mesh Circuit Analysis

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