Kirchhoff's circuit laws are a pair of laws that deal with the conservation of charge and energy in electrical circuits, and were first described in 1845 by Gustav Kirchhoff. Widely used in electrical engineering, they are also called Kirchhoff's rules or simply Kirchhoff's laws (see also Kirchhoff's laws for other meanings of that term). An electrical network or electrical circuit is an interconnection of analog electrical elements such as resistors, inductors, capacitors, diodes, switches and transistors. ... 1845 was a common year starting on Wednesday (see link for calendar). ... Gustav Robert Kirchhoff (March 12, 1824 - October 17, 1887), a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects. ... Electrical engineering is an engineering discipline that deals with the study and application of electricity and electromagnetism. ...

Both circuit rules can be directly derived from the Maxwell's equations, but Kirchhoff preceded Maxwell and instead generalized work by Georg Ohm. Maxwells equations are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ... James Clerk Maxwell James Clerk Maxwell (June 13, 1831 - November 5, 1879) was a Scottish physicist, born in Edinburgh. ... Georg Simon Ohm, (Erlangen March 16, 1787 or 1789 - Munich July 6, 1854), German physicist, was born in Erlangen and educated at the university there. ...

Kirchhoff's current law

i₁ + i₄ = i₂ + i₃

This law is also called Kirchhoff's first law, Kirchhoff's point rule, Kirchhoff's junction rule, and Kirchhoff's first rule.

The principle of conservation of electric charge implies that: Electric charge is a fundamental property of some subatomic particles, which determines their electromagnetic interactions. ...

At any point in an electrical circuit where charge density is not changing in time, the sum of currents flowing towards that point is equal to the sum of currents flowing away from that point.

A charge density changing in time would mean the accumulation of a net positive or negative charge, which typically cannot happen to any significant degree because of the strength of electrostatic forces: the charge buildup would cause repulsive forces to disperse the charges. An electrical network or electrical circuit is an interconnection of analog electrical elements such as resistors, inductors, capacitors, diodes, switches and transistors. ... In electricity, current is the rate of flow of charges, usually through a metal wire or some other electrical conductor. ...

However, a charge buildup can occur in a capacitor, where the charge is typically spread over wide parallel plates, with a physical break in the circuit that prevents the positive and negative charge accumulations over the two plates from coming together and cancelling. In this case, the sum of the currents flowing into one plate of the capacitor is not zero, but rather is equal to the rate of charge accumulation. However, if the displacement current dD/dt is included, Kirchhoff's current law once again holds. (This is only required if one wants to apply the current law within the capacitor. In circuit analyses, however, the capacitor as a whole is typically treated as a unit, in which case the ordinary current law holds since the net charge is always zero.) Various types of capacitors A capacitor is a device that stores energy in the electric field created between a pair of conductors on which equal but opposite electric charges have been placed. ... Displacement current is a pseudocurrent invented in 1865 by James Clerk Maxwell when formulating what are today known as Maxwells equations. ...

More technically, Kirchhoff's current law can be found by taking the divergence of Ampere's law with Maxwell's correction and combining with Gauss's law, yielding: In vector calculus, the divergence is an operator that measures a vector fields tendency to originate from or converge upon a given point. ... In physics, Ampères law is the magnetic equivalent of Gausss law, discovered by André-Marie Ampère. ... In physics, Gausss law gives the relation between the electric flux flowing out a closed surface and the charge enclosed in the surface. ...

This is simply the charge conservation equation (in integral form, it says that the current flowing out of a closed surface is equal to the rate of loss of charge within the enclosed volume). Kirchhoff's current law is equivalent to the statement that the divergence of the current is zero, true for time-invariant ρ, or always true if the displacement current is included with J.

Kirchhoff's voltage law

v₁ + v₂ + v₃ + v₄ = 0

This law is also called Kirchhoff's second law, Kirchhoff's loop rule, and Kirchhoff's second rule.

The principle of conservation of energy implies that: Conservation of energy (the first law of thermodynamics) is one of several conservation laws. ...

The directed sum of the electrical potential differences around a circuit must sum to zero.

(Otherwise, it would be possible to build a perpetual motion machine that passed a current in a circle around the circuit.) In the physical sciences, potential difference is the difference in potential between two points in a conservative vector field. ... This article or section should include material from Parallel Path See also Perpetuum mobile as a musical term Perpetual motion machines (the Latin term perpetuum mobile is not uncommon) are a class of hypothetical machines which would produce useful energy in a way science cannot explain (yet). ...

This law has a subtlety in its interpretation, because in the presence of a changing magnetic field the electric field is not conservative and it cannot therefore define a pure scalar potential—the line integral of the electric field around the circuit is not zero. Equivalently, energy is being transferred from the magnetic field to the current (or vice versa). In order to "fix" Kirchhoff's voltage law for this case, an effective potential drop, or electromotive force (emf), is associated with the inductance of the circuit, exactly equal to the amount by which the line integral of the electric field is not zero by Faraday's law of induction. In physics, a magnetic field is an entity produced by moving electric charges (electric currents) that exerts a force on other moving charges. ... In physics, an electric field or E-field is an effect produced by an electric charge that exerts a force on charged objects in its vicinity. ... Conservatism or political conservatism is any of several historically related political philosophies or political ideologies. ... In physics, a potential is a scalar quantity that can be used to analyze the effects of complicated vectorial forces and similar quantities by means of simple conservation laws. ... An electromotive force (emf) is the force, measured in volts, that is produced by interaction between a current and a magnetic field, at least one of which is changing. ... Inductance is a physical characteristic of an inductor, which is an electrical device that produces at any time a voltage proportional to the instantaneous rate of change in current flowing through it. ...

See also

• Analysis of resistive circuits
• Y-delta transform

A resistive circuit is a circuit containing only resistors, perfect current sources, and perfect voltage sources. ... The Y-delta transform (also written Wye-delta transform or Kennellys Delta-Star transformation) or star-mesh transformation is a technique to simplify analysis of an electrical network. ...

External links

• 2 laws (http://www.phys.ualberta.ca/~gingrich/phys395/notes/node10.html)
• http://www.sasked.gov.sk.ca/docs/physics/u3c13phy.html