Name: ac circuit phasors: resistor, inductor, capacitor
Uploaded: 2024-04-11T12:48:48.000Z
Duration: 1 min 16 s
Channel: JoVE

يمكن تحويل علاقة الجهد والتيار للمقاومات والمحاثات والمكثفات من المجال الزمني إلى مجال الطور أو مجال التردد باستخدام تمثيل الطور.
في المجال الزمني ، يوفر قانون أوم علاقة بين التيار المتدفق عبر المقاوم والجهد عبره.
وبالمثل ، في تمثيل الطور ، يكون الجهد والتيار في طور ويتبعان قانون أوم.
بالنسبة للمحث ، فإن معدل تغير التيار يعطي الجهد عبره. يتم تحويل الوظيفة الجيبية إلى مرحلتها في شكل قطبي.
بمقارنة مراحل التيار والجهد ، يتأخر التيار عن الجهد بمقدار 90 درجة.
باستخدام هوية أويلر ، يتم الحصول على علاقة التيار والجهد في مجال الطور.
وبالمثل ، عند شحن مكثف ، يحدد معدل تغير الجهد التيار الذي يمر عبره ، ويتم استخدام الوظيفة الجيبية للحصول على طورها في شكل قطبي.
تشير تمثيلات الطور إلى أن التيار يؤدي إلى الجهد بمقدار 90 درجة ، ويمكن الحصول على العلاقة بين مراحل التيار والجهد عن طريق استبدال المشتق الزمني للجهد.

العلاقات الطورية لعناصر الدائرة

<div style="direction:rtl">يعد تمثيل Phasor أداة قوية تستخدم لتحويل العلاقة بين الجهد والتيار للمقاومات والمحاثات والمكثفات من المجال الزمني إلى مجال التردد يبسط هذا التحويل تحليل دوائر التيار المتردد. في المجال الزمني، يوفر قانون أوم علاقة أساسية بين التيار المتدفق عبر المقاومة والجهد عبرها: <img alt="Equation1" src="/files/ftp_upload/15107/15107_PT_Equation_1.svg" style="text-align: center; height: 12px;"> حيث V هو الجهد، I هو التيار، و R هي المقاومة. في التمثيل الطوري، تكون هذه العلاقة صحيحة أيضا، حيث يكون أطوار الجهد والتيار في الطور ويتبعان قانون أوم. بالنسبة للمحرض، فإن العلاقة بين الجهد عبره والتيار المتدفق من خلاله يتم تحديدها من خلال معدل تغير التيار. يمكن تحويل الدالة الجيبية التي تمثل هذه العلاقة إلى طورها بالتنسيق القطبي. عند مقارنة مراحل التيار والجهد لمحرض، يمكن ملاحظة أن التيار يتخلف عن الجهد بمقدار 90 درجة. باستخدام هوية أويلر، وهي صيغة أساسية في التحليل المعقد، يمكن الحصول على العلاقة بين التيار والجهد في مجال الطور. وبالمثل، عند شحن مكثف، فإن التيار الذي يمر عبره يتحدد بمعدل تغير الجهد عبره. مرة أخرى، يمكن تحويل الدالة الجيبية التي تمثل هذه العلاقة إلى طورها في الشكل القطبي. في حالة المكثف، تشير تمثيلات الطور إلى أن التيار يقود الجهد بمقدار 90 درجة. يمكن الحصول على العلاقة بين مراحل التيار والجهد للمكثف باستخدام المشتق الزمني للجهد.</div>

يمكن تحويل علاقة الجهد والتيار للمقاومات والمحاثات والمكثفات من المجال الزمني إلى مجال الطور أو التردد ...

phasor-relationships-for-circuit-elements

Education

JoVE Core

Electrical Engineering

الهندسة الكهربائية

Unit 1

الوحدة الأولى

AC Circuit Analysis

تحليل دوائر التيار المتردد

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الرئيسية

Phasor Relationships for Circuit Elements

ac circuit phasors: resistor, inductor, capacitor

AC circuit phasors help show how voltage and current behave for resistors, inductors, and capacitors. Phasor representation moves these relationships from the time domain to the frequency domain, which makes AC circuit analysis easier.

For a resistor, Ohm's law still applies. The voltage across the resistor and the current through it stay in phase, so their phasors point in the same direction.

An inductor works differently because its voltage depends on the rate of change of current. The sinusoidal form of this relationship can be written as a phasor in polar form. When the voltage and current phasors are compared, the current lags the voltage by 90 degrees. Euler's identity is used to obtain the current-voltage relationship in the phasor domain.

A capacitor also depends on change, but here the current depends on the rate of change of voltage across it. Its sinusoidal form can also be converted into a phasor in polar form. For a capacitor, the current leads the voltage by 90 degrees. The time derivative of the voltage is used to derive the current-voltage relationship for the phasor form.

AC Circuit Phasors: Resistor, Inductor, Capacitor

ac-circuit-phasors-resistor-inductor-capacitor

sinusoidal sources

AC Waveform Basics and Phase

Alternating current, or AC, changes direction and magnitude over time, unlike direct current, or DC, which flows in one direction with constant polarity. AC is the main form of electricity used for modern power transmission and distribution because it can travel long distances efficiently. In homes, power supplies use sinusoidal sources to deliver electricity. A sinusoidal source creates a voltage that rises and falls in a smooth wave-like pattern. This waveform is called a sinusoid, which is...

graphical and analytic representation of sinusoids

graphical-and-analytic-representation-of-sinusoids

Measuring Sinusoid Phase on an Oscilloscope

Measuring sinusoid phase on an oscilloscope helps compare two sinusoidal voltages with the same amplitude and period. An oscilloscope is an instrument used to display and analyze waveforms. The process starts by reading the peak-to-peak value, which is twice the amplitude of the sinusoid. This shows the maximum voltage swing of the waveform. Next, the period and angular frequency are measured. The period is the time for one complete cycle. Angular frequency, often written as omega, is the rate...

phasors

Phasors for AC Circuit Analysis

Phasors are a mathematical tool for analyzing alternating current, or AC, circuits. They represent sinusoids with complex numbers. The phasor magnitude matches the sinusoid amplitude, and the phasor angle shows the phase measured from the positive x-axis. Phasors make AC circuit analysis simpler by removing time from the current and voltage expressions. That lets an AC circuit be treated like its equivalent direct current, or DC, form for calculations. Phasors can also be written in...

phasor arithmetics

Phasor Rules for AC Circuit Analysis

Phasor rules make AC circuit analysis easier by linking sinusoids to their matching phasors. A phasor is a complex-number form of a sinusoidal signal. This connection helps explain how alternating current changes with time. Differentiation and integration work in both the time domain and the phasor domain. If you take the derivative of a sinusoid in time, its phasor is multiplied by jω, where j is the imaginary unit and ω is the angular frequency. If you integrate a sinusoid in time, its...

phasor relationships for circuit elements

AC circuit phasors help show how voltage and current behave for resistors, inductors, and capacitors. Phasor representation moves these relationships from the time domain to the frequency domain, which makes AC circuit analysis easier. For a resistor, Ohm's law still applies. The voltage across the resistor and the current through it stay in phase, so their phasors point in the same direction. An inductor works differently because its voltage depends on the rate of change of current. The...

kirchoff's laws using phasors

AC Circuit Rules with Phasor Diagrams

AC circuit analysis uses Kirchhoff's voltage law and Kirchhoff's current law with phasors. In household wiring, AC power from a distribution panel is sent to appliances connected in parallel. These rules help describe how voltage and current behave in sinusoidal steady state. Kirchhoff's voltage law, or KVL, says that the sum of phasor voltages around a closed loop in an AC circuit is zero. The voltages can first be written in the time domain and then changed into phasor form. In phasor...

impedances and admittance

AC Circuit Response: Impedance and Admittance

AC circuit response changes with frequency, and impedance describes how resistors, inductors, and capacitors affect sinusoidal current flow. In phasor form, voltage and current are used to show this behavior in a clear way. Impedance is a key idea in AC circuit analysis because it measures opposition to current in an alternating circuit. These components behave differently in AC than in DC. In DC circuits, inductors act like short circuits and capacitors act like open circuits. In AC circuits,...

impedance combination

Series and Parallel Impedance Rules

Impedance in series and parallel circuits follows the same rules used for resistors. A string of Christmas lights is a simple example. Each bulb represents one impedance element. In a series connection, the current stays the same through every component. This series behavior matches Kirchhoff’s Voltage Law, or KVL. The total impedance in the circuit is the sum of the individual impedances. The source voltage is then divided among the components based on their values. This is the voltage...

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AC Circuit Node Method in an Angioplasty Model

AC circuit node analysis is used to study an angioplasty system with a catheter turbine. The system helps remove plaque deposits from coronary arteries. Its electrical model is similar to a dual-node RLC circuit driven by a current-controlled voltage source. The analysis begins by collecting the input source voltage, inductance, and capacitance values. These measurements are used to find the driving voltage for the catheter shaft. The circuit is then viewed in the frequency domain, where...

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Impedance Matching with Mesh Currents

Impedance matching in radio communication uses resistor, capacitor, and inductor circuits to help signals move efficiently between a transmitter and a receiver. The circuit must balance the input and output signals before the current in the capacitor can be found. This makes the problem a good example of AC circuit analysis for high school students. The first step is to identify the input voltage and the output signal. The angular frequency is then taken from the time-domain form of the input...

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AC Source Conversion in Circuit Analysis

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Finding Voltage and Impedance in Circuit A

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norton equivalent circuits

Norton Current in AC Circuit Analysis

Norton’s theorem helps simplify complex AC circuits by replacing a two-terminal linear network with a smaller equivalent circuit. That equivalent circuit uses an impedance in parallel with a constant current source. The method lets students break one complicated circuit into two parts and analyze them more easily. To build the Norton equivalent, the source is replaced by its internal impedance. The result is the Norton impedance, which is the same as the Thévenin impedance. This parallel...

superposition theorem for ac circuits

Analyzing Mixed-Frequency Linear Circuits

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Analyzing an Op Amp Audio Filter

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Capacitance Multiplier Circuit for Larger Capacitance

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key terms and concepts

Learn how phasors describe AC circuit behavior in resistors, inductors, and capacitors, including in-phase signals and 90-degree lead or lag.

AC Circuit Phasors: Resistor, Inductor, Capacitor | 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

AC Circuit Phasors: Resistor, Inductor, Capacitor

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