Name: rc capacitor discharge after power loss
Uploaded: 2024-04-11T12:48:43.000Z
Duration: 1 min 16 s
Channel: JoVE

عندما تتم إزالة مصدر التيار المستمر فجأة من دائرة RC ، تصبح الدائرة خالية من المصدر.
بافتراض أن الجهد الأولي للمكثف المشحون بالكامل هو V0 ، يمكن الحصول على طاقته الأولية التي تحفز الدائرة.
إن تطبيق قانون كيرشوف الحالي في العقدة العلوية واستبدال القيم الحالية عبر المكونات يعطي معادلة تفاضلية من الدرجة الأولى.
تؤدي إعادة ترتيب المصطلحات والتكامل وأخذ الأس على كلا الجانبين إلى الاستجابة الطبيعية للدائرة ، حيث يساوي ثابت التكامل الجهد الأولي.
يوضح الرسم البياني للجهد مقابل الوقت أن الجهد الأولي يتحلل بشكل كبير مع مرور الوقت.
يشير ثابت الوقت ، تاو ، إلى الوقت اللازم للمكثف لتفريغه إلى 36.8 بالمائة من جهده الأولي.
من خلال استبدال قيمة تاو في تعبير استجابة الجهد ، يمكن تحديد التيار والطاقة المتبددة في المقاوم.
يوفر دمج الطاقة المشتتة بمرور الوقت الطاقة التي يمتصها المقاوم.
مع اقتراب الوقت من اللانهاية ، تقترب هذه الطاقة من الطاقة الأولية المخزنة في المكثف ، مما يعني أن الطاقة الأولية للمكثف تتبدد تدريجيا في المقاوم.

لم يتم الإعلان عن أي تضارب في المصالح.

دارة rc دون مصدر

RC Circuit without Source

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عندما يتم فصل مصدر التيار المستمر بشكل مفاجئ عن دائرة RC (المقاوم-المكثف)، تصبح الدائرة خالية من المصدر. بافتراض أن المكثف كان مشحونًا بالكامل قبل إزالة المصدر، فإن جهده الأولي، المشار إليه بـ V0، يمكن اعتباره الطاقة الأولية التي تحفز الدائرة.

وبتطبيق قانون كيرشوف للتيار على العقدة العليا للدائرة واستبدال القيم الحالية عبر المكونات، يتم الحصول على معادلة تفاضلية من الدرجة الأولى. من خلال إعادة ترتيب الحدود في هذه المعادلة، والتكامل، ثم أخذ الأسي على كلا الجانبين، يتم تحديد الاستجابة الطبيعية للدائرة. ثابت التكامل في هذه المعادلة يساوي الجهد الأولي.

يوضح الرسم البياني للجهد مقابل الوقت أن الجهد الأولي يتضاءل بشكل كبير مع مرور الوقت. وهذا يعني أن شحنة المكثف تتناقص تدريجياً، مما يؤدي بدوره إلى تقليل الجهد عبره.

يشير الثابت الزمني للدائرة، والذي يمثله الحرف اليوناني tau (τ)، إلى الوقت اللازم لتفريغ المكثف إلى 36.8% من جهده الأولي. يلعب هذا الثابت الزمني دورًا حاسمًا في تحديد معدل تفريغ المكثف، ونتيجة لذلك، السرعة التي تستجيب بها الدائرة للتغيرات.

من خلال استبدال قيمة تاو في تعبير استجابة الجهد، يمكن حساب التيار المتدفق عبر المقاومة، وكذلك الطاقة المتبددة في المقاومة. الطاقة المتبددة في المقاومة هي معدل فقدان الطاقة على شكل حرارة.

إن دمج الطاقة المتبددة بمرور الوقت يوفر إجمالي الطاقة التي يمتصها المقاوم. ومع اقتراب الوقت من اللانهاية، تقترب هذه الطاقة من الطاقة الأولية المخزنة في المكثف. وهذا يعني أن الطاقة الأولية للمكثف تتبدد تدريجياً في المقاومة، مما يؤدي في النهاية إلى استنفاد شحنة المكثف.

في الختام، فإن فهم سلوك دوائر RC عند إزالة مصدر التيار المستمر يوفر رؤى قيمة حول الاستجابة العابرة لهذه الدوائر. هذه المعرفة ضرورية لتصميم وتحليل الدوائر في تطبيقات مثل معالجة الإشارات، وإلكترونيات الطاقة، وأنظمة الاتصالات، حيث يعد الشحن والتفريغ السريع للمكثفات عملية أساسية.
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دارة RC دون مصدر

عندما تتم إزالة مصدر التيار المستمر فجأة من دائرة RC ، تصبح الدائرة خالية من المصدر.
بافتراض أن الجهد الأولي للمكثف المشحون بالكامل هو ...

Education

JoVE Core

Electrical Engineering

الهندسة الكهربائية

Unit 1

الوحدة الأولى

First and Second-Order Circuits

الدوائر ذات الرتبة الأولى والثانية

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

rc capacitor discharge after power loss

An RC circuit discharges after the DC source is removed. If the capacitor was fully charged first, its initial voltage, V0, provides the energy that drives the source-free circuit.

Kirchhoff’s current law is applied at the top node of the circuit. The current terms for the resistor and capacitor are then substituted, which leads to a first-order differential equation. Rearranging, integrating, and taking the exponential gives the natural response of the circuit. The integration constant in this expression equals the initial voltage.

The voltage-time graph shows an exponential drop in voltage. As the capacitor loses charge, the voltage across it also falls. The time constant, tau (τ), is the time needed for the capacitor to discharge to 36.8% of its initial voltage. It helps determine how fast the capacitor discharges and how quickly the circuit responds to change.

Using tau in the voltage response expression also allows the current through the resistor to be found. From that current, the power dissipated in the resistor can be calculated. Power is the rate at which energy is lost as heat. When that power is integrated over time, the total energy absorbed by the resistor is obtained.

As time approaches infinity, the energy absorbed by the resistor approaches the initial energy stored in the capacitor. In other words, the capacitor’s initial energy is gradually converted into heat in the resistor until the charge is depleted. Understanding this transient response is useful for analyzing RC circuits in signal processing, power electronics, and communication systems, where capacitor charging and discharging are key processes.

RC Capacitor Discharge After Power Loss

first-order circuits

First-Order Circuits in Flashing Lamps

First-order circuits use a resistor and one energy storage element, either a capacitor or an inductor. They are common in electronic systems and are described by a first-order differential equation that links the input and output signals. One important example is the RC circuit, which uses a resistor and a capacitor. In a relaxation oscillator such as a neon lamp circuit, the capacitor starts charging when voltage is applied. At first, the lamp behaves like an open circuit. When the capacitor...

rc circuit without source

An RC circuit discharges after the DC source is removed. If the capacitor was fully charged first, its initial voltage, V0, provides the energy that drives the source-free circuit. Kirchhoff’s current law is applied at the top node of the circuit. The current terms for the resistor and capacitor are then substituted, which leads to a first-order differential equation. Rearranging, integrating, and taking the exponential gives the natural response of the circuit. The integration constant in...

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second-order circuits

RLC Damping and Resonant Frequency

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Natural Response of a Source-Free RLC Circuit

A source-free RLC circuit is a series circuit with a resistor, inductor, and capacitor, but no external energy source. It begins with the energy already stored in the capacitor and inductor. That stored energy drives the circuit at first. The circuit is described by a second-order differential equation. This equation shows how the resistor, inductor, and capacitor interact over time. The resistor removes energy from the circuit, so the solution has an exponential form. When the exponential...

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types-of-responses-of-series-rlc-circuits

Damping in Series RLC Circuit Responses

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Forced Response in a Series RLC Circuit

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key terms and concepts

Learn how a source-free RC circuit discharges after the DC source is removed, including exponential voltage decay, time constant, current, and energy loss.

RC Capacitor Discharge After Power Loss | 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

RC Capacitor Discharge After Power Loss

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