Name: series resistors and voltage split
Uploaded: 2024-04-11T12:48:28.000Z
Duration: 1 min 14 s
Channel: JoVE

При последовательном соединении резисторы последовательно соединены, и через каждый из них должен протекать одинаковый ток.
Напряжение на этих резисторах может быть выражено с помощью закона Ома. Согласно закону напряжения Кирхгофа, сумма напряжения на резисторах равна напряжению источника.
В результате ток в цепи равен напряжению источника, деленному на общее сопротивление последовательно.
Подставляя выражение тока в закон Ома, мы получаем напряжение на каждом резисторе.
Таким образом, напряжение источника пропорционально распределяется между несколькими резисторами в соответствии с их индивидуальными сопротивлениями, что известно как принцип «деления напряжения». Цепь, демонстрирующая этот принцип, называется делителем напряжения.
Комбинацию резисторов, соединенных последовательно, можно рассматривать как один эквивалентный резистор.
Сопротивление этого эквивалентного резистора равно сумме сопротивлений отдельных резисторов, идущих последовательно.
Эквивалентное сопротивление может быть обобщено для любого числа последовательно соединенных резисторов.
Аналогичным образом можно записать обобщенное выражение для падения напряжения на этих резисторах.

Делители напряжения

В электрических цепях резисторы могут соединяться последовательно, друг за другом. В последовательной конфигурации через каждый резистор течет одинаковый ток. Закон Ома является фундаментальным принципом для понимания поведения резисторов, включенных последовательно. Он выражает напряжение на этих резисторах через ток и сопротивление.

Закон Кирхгофа подразумевает, что сумма напряжений на последовательно соединенных резисторах равна напряжению источника. Это означает, что ток в цепи равен напряжению источника, деленному на общее сопротивление последовательного соединения. Это выражение тока можно подставить в закон Ома, чтобы определить напряжение на каждом резисторе. Такое расположение приводит к пропорциональному разделению напряжения источника между несколькими резисторами в зависимости от их индивидуальных сопротивлений. Этот принцип известен как «деление напряжения», а схема, иллюстрирующая этот принцип, называется «делителем напряжения».

Комбинацию резисторов, соединенных последовательно, можно рассматривать как один эквивалентный резистор. Значение этого эквивалентного резистора представляет собой просто сумму сопротивлений отдельных резисторов, включенных последовательно. Эта концепция распространяется на любое количество резисторов, соединенных последовательно.

<img alt="Equation1" src="/files/ftp_upload/15072/15072_PT_Equation_1.svg" style="text-align: center; height: 16px;" />

Падение напряжения на каждом резисторе в последовательной цепи прямо пропорционально его сопротивлению. В результате резисторы с большими значениями сопротивления будут испытывать более значительные падения напряжения. Этот принцип лежит в основе делителей напряжения, где падение напряжения на каждом резисторе определяется его сопротивлением относительно общего сопротивления в последовательной цепи.

На практике широко распространено объединение резисторов последовательно или параллельно, что часто требует упрощенного представления схемы. Такое упрощение достигается за счет объединения двух резисторов одновременно. Эквивалентное сопротивление двух резисторов, включенных последовательно, представляет собой сумму их индивидуальных сопротивлений. Этот метод облегчает анализ сложных цепей, предоставляя инженерам ценный инструмент для проектирования и устранения неисправностей электрических систем.

При последовательном соединении резисторы последовательно соединены, и через каждый из них должен протекать одинаковый ток.
Напряжение на этих резисторах может быть ...

Education

JoVE Core

Electrical Engineering

Электротехника

Unit 1

Раздел 1

Basics of Electric Circuits

Основы электрических цепей

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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 law to find the voltage across each resistor. This is the principle of voltage division.

A circuit that uses this principle is called a voltage divider. The source voltage is shared among the resistors in proportion to their resistance values. A resistor with a larger resistance gets a larger voltage drop. This relationship stays the same for any number of resistors in series.

Resistors in series can also be replaced by one equivalent resistor. Its resistance is the sum of the individual resistances. Circuit analysis often uses this idea when simplifying complex networks. Engineers combine two resistors at a time to make the circuit easier to study and troubleshoot.

Series Resistors and Voltage Split

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

Circuit sources in electrical circuits can be independent or dependent. They provide the power a circuit needs to operate. Independent voltage sources supply a fixed voltage, and independent current sources supply a fixed current. Their output does not change because of other parts in the circuit. These sources use standard symbols in circuit diagrams. An independent voltage source is shown with + and - signs to mark the potential difference. An independent current source is shown with an...

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 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

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 resistors in series split source voltage, use Ohm's law and Kirchhoff's voltage law, and simplify circuits with equivalent resistance.

Series Resistors and Voltage Split | 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

Series Resistors and Voltage Split

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