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

直列接続では、抵抗は順番にリンクされ、それぞれに同じ電流が流れる必要があります。
これらの抵抗器の両端の電圧は、オームの法則を使用して表すことができます。キルヒホッフの電圧法則によれば、抵抗器の両端の電圧の合計は電源電圧に等しくなります。
その結果、回路内の電流は、ソース電圧を直列の合計抵抗で割った値に等しくなります。
オームの法則で電流式を代入すると、各抵抗の両端の電圧が得られます。
そのため、電源電圧は複数の抵抗器の個々の抵抗値に応じて比例して分圧され、これを「分圧器」の原理として知られています。この原理を示す回路を分圧器と呼びます。
直列に接続された抵抗の組み合わせは、1つの等価抵抗として扱うことができます。
この等価抵抗の抵抗は、直列の個々の抵抗の抵抗の合計に等しくなります。
等価抵抗は、直列に接続された任意の数の抵抗に対して一般化できます。
同様に、これらの抵抗の両端の電圧降下の一般化された式を書くことができます。

分圧器

電気回路では、抵抗器を直列に接続し、次々に接続することができます。直列構成では、各抵抗器に同じ電流が流れます。オームの法則は、直列抵抗器の動作を理解するための基本原則です。これらの抵抗にかかる電圧を電流と抵抗で表します。

キルヒホッフの電圧の法則は、直列抵抗器の両端の電圧の合計が電源電圧に等しいことを意味します。これは、回路内の電流が電源電圧を直列の合計抵抗で割ったものに等しいことを意味します。この電流式をオームの法則に代入して、各抵抗の両端の電圧を決定できます。この配置により、個々の抵抗に基づいて複数の抵抗間で電源電圧が比例分割されます。この原理は分圧として知られ、それを利用する回路を分圧器と呼びます。

直列に接続された抵抗の組み合わせは、単一の等価抵抗として扱うことができます。この等価抵抗の値は、単に直列に接続された個々の抵抗の抵抗値の合計です。この概念は、直列に接続された任意の数の抵抗器に拡張されます。

<img alt="Equation1" src="/files/ftp_upload/15072/15072_PT_Equation_1.svg" style="text-align: center; height: 16px;">

直列回路内の各抵抗の両端の電圧降下は、その抵抗に正比例します。その結果、抵抗値が大きい抵抗では、より大きな電圧降下が発生します。この原理は分圧器の中核であり、各抵抗の電圧降下は、直列の合計抵抗に対する相対的な抵抗によって決まります。

実際には、抵抗を直列や並列に組み合わせて、回路を簡略化することが一般的です。この簡素化は、一度に 2 つの抵抗を組み合わせることで実現されます。直列の 2 つの抵抗の等価抵抗は、それぞれの抵抗の合計です。この技術は複雑な回路の解析を容易にし、エンジニアに電気システムの設計とトラブルシューティングのための貴重なツールを提供します。

直列接続では、抵抗は順番にリンクされ、それぞれに同じ電流が流れる必要があります。
これらの抵抗器の両端の電圧は...

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

Basics of Electric Circuits

電気回路の基礎

KEY TERMS AND CONCEPTS

主要用語および概念

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 電気工学 は、電気回路の基本概念と回路解析テクニックを網羅したアニメーションビデオシリーズです。オペアンプと回路変換および 1 次・ 2 次回路の概念を網羅しています。実験を撮影した実写動画では、設計例や現代社会での応用が含まれており、複雑な概念も分かりやすく学習いただけます。

electrical engineering

Series Resistors and Voltage Split

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