Cecily Zamora
In 1845, German physicist Gustav Kirchhoff developed a pair of laws that deal with the conservation of current and energy within electrical circuits. These laws, commonly known as Kirchhoff's Voltage and Current Law, are two equalities that apply to the current and potential difference in the lumped element model of electrical circuits. Both of Kirchhoff's laws can be understood as corollaries of Maxwell's equations in the low-frequency limit. They are accurate for DC circuits and for AC circuits at frequencies where the wavelengths of electromagnetic radiation are very large compared to the circuits. Kirchhoff's Current Law states that the total current entering a junction or node equals the charge leaving the node, as no charge is lost. Kirchhoff's Voltage Law states that the voltage around a loop equals the sum of every voltage drop in the same loop for any closed network and equals zero.
| Characteristics | Values |
|---|---|
| Name | Kirchhoff's Laws, Kirchhoff's Circuit Laws, Kirchhoff's Rules, Kirchhoff's Voltage and Current Laws |
| Purpose | To deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits |
| Inventor | Gustav Kirchhoff |
| Year | 1845 |
| Number of Laws | 2 |
| First Law | Kirchhoff's Current Law, Kirchhoff's First Law, Kirchhoff's Junction Rule |
| First Law Description | The total current entering a junction or node equals the charge leaving the node as no charge is lost |
| Second Law | Kirchhoff's Voltage Law, Kirchhoff's Second Law, Kirchhoff's Loop Rule |
| Second Law Description | The voltage around a closed loop equals the sum of every voltage drop in the loop and equals zero |
| Application | Applicable to all electric circuits, DC circuits, AC circuits with low frequencies |
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What You'll Learn
Kirchhoff's Current Law
This law is based on the assumption that the net charge in any wire, junction, or lumped component is constant. It is used to determine the amount or magnitude of the electrical current flowing around an electrical or electronic circuit. By applying Kirchhoff's Current Law, we can write down these currents in the form of an equation.
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Kirchhoff's Voltage Law
When applying Kirchhoff's Voltage Law to a specific circuit element, it is important to pay attention to the algebraic signs of the voltage drops across elements and the emf's of sources, or the polarities and signs of the sources and voltage drops around the loop. The direction of the current flowing through a resistive element will determine the sign of the voltage drop across it.
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Conservation of charge
In 1845, German physicist Gustav Kirchhoff formulated two laws that apply to all electric circuits: the conservation of current (Kirchhoff's Current Law, or KCL) and the conservation of energy (Kirchhoff's Voltage Law, or KVL).
Kirchhoff's Current Law, or Kirchhoff's First Law, states that the total current entering a junction or node equals the charge leaving the node. In other words, no charge is lost. This is commonly referred to as the conservation of charge, wherein I(exit) + I(enter) = 0.
In a circuit, a node refers to a junction connecting two or more current-carrying routes, such as cables and other components. Kirchhoff's Current Law can be applied to analyse parallel circuits. It can also be used to solve circuit problems by applying the Junction Rule, which states that the sum of the currents into a junction equals the sum of the currents out of a junction.
Kirchhoff's Voltage Law, or Kirchhoff's Second Law, states that the voltage around a closed loop equals the sum of every voltage drop in the same loop and equals zero. This is commonly referred to as the conservation of energy, wherein the algebraic sum of every voltage in the loop has to be equal to zero.
Kirchhoff's two laws are foundational to circuit analysis, providing rules that can be applied to analyse any circuit, simple or complex.
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Conservation of energy
Kirchhoff's circuit laws, also known as Kirchhoff's rules, are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchhoff. These laws can be applied to any circuit, simple or complex, and form the basis for network analysis.
Kirchhoff's rules are applications of conservation laws to circuits. The first rule, also known as the junction rule, is the application of conservation of charge. This rule states that the sum of all currents entering a junction or node equals the charge leaving the node, as no charge is lost.
The second rule, also known as the loop rule, is an application of conservation of energy. This rule states that the algebraic sum of the voltage differences around any closed loop or circuit path is equal to zero. In other words, the voltage around a loop equals the sum of every voltage drop in the same loop for any closed network and equals zero.
By applying Kirchhoff's rules, we can generate a set of linear equations that allow us to find unknown values in circuits, such as currents, voltages, or resistances. Kirchhoff's rules are widely used in electrical engineering and can be applied to devices such as resistors, capacitors, and emfs. They are considered special cases of the laws of conservation of charge and conservation of energy.
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Application to complex circuits
Kirchhoff's laws, also known as Kirchhoff's Circuit Law, are widely applied to complex circuits. These laws were formulated by Gustav Kirchhoff, a German physicist, in 1845. They are used to analyse the current and voltage in complex electrical circuits.
Ohm's Law is a simple method for calculating voltage, current, and resistance in a basic series or parallel circuit. However, in complex circuits, Ohm's Law may not be sufficient, and Kirchhoff's Laws become useful. Kirchhoff's Laws can be applied to any circuit, whether simple or complex, and they are especially valuable when a circuit includes both series and parallel resistance or when there is no constant current source.
Kirchhoff's Current Law (KCL), also known as Kirchhoff's First Law, states that the total current entering a junction or node equals the total current leaving the node. This is based on the principle of the conservation of charge, where the algebraic sum of currents entering and leaving a node is zero. In other words, the current entering a node must exit the node, as there is nowhere else for it to go. This law can be applied to analyse parallel circuits.
Kirchhoff's Voltage Law (KVL), or Kirchhoff's Second Law, states that the algebraic sum of the voltages in a closed network or loop is zero. This is based on the conservation of energy, where the voltage around a loop equals the sum of every voltage drop in the same loop. This law can be applied to analyse series circuits.
When combined, Kirchhoff's Current Law and Kirchhoff's Voltage Law form Kirchhoff's Circuit Law, which allows for the analysis of both current and voltage in complex circuits. This is achieved by creating a system of linear equations to calculate the current and voltage.
Kirchhoff's rules can be used to analyse any circuit, and they are derived from the fundamental conservation laws of physics. The first rule, the junction rule, is an application of the conservation of charge, where the sum of currents entering a junction equals the sum of currents leaving it. The second rule, the loop rule, is an application of the conservation of energy, where the algebraic sum of changes in potential around a closed loop is zero.
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Frequently asked questions
Kirchhoff's laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits.
Kirchhoff's laws are both applications of conservation laws to circuits. The first rule is the application of conservation of charge, while the second rule is the application of conservation of energy.
Kirchhoff's first rule is also known as the junction rule, while the second rule is known as the loop rule.
