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). In cryptography, Kerckhoffs principle (also called Kerckhoffs assumption, axiom or law) was stated by Auguste Kerckhoffs in the 19th century: a cryptosystem should be secure even if everything about the system, except the key, is public knowledge. ... Charge conservation is the principle that electric charge can neither be created nor destroyed. ... 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 Kirchhof (March 12, 1824 – October 17, 1887) was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects. ... Electrical Engineers design power systems… … and complex electronic circuits. ... There are several Kirchhoffs laws, all named after Gustav Robert Kirchhoff: Kirchhoffs circuit laws Kirchhoffs law of thermal radiation Kirchhoffs Three Empirical Laws of Spectroscopy Scientific laws named after people Category: ...

Both circuit rules can be directly derived from Maxwell's equations, but Kirchhoff preceded Maxwell and instead generalized work by Georg Ohm. For thermodynamic relations, see Maxwell relations. ... James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and theoretical physicist from Edinburgh, Scotland, UK. His most significant achievement was aggregating a set of equations in electricity, magnetism and inductance — eponymously named Maxwells equations — including an important modification (extension) of the Ampères... Georg Simon Ohm (March 16, 1789 - July 6, 1854) was a German physicist. ...

Kirchhoff's Current Law (KCL)

The current entering any junction is equal to the current leaving that junction. 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. Image File history File links Kirchoffs Current Law File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...

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

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. ... Charge density is the amount of electric charge per unit volume. ... In electricity, current refers to electric current, which is the flow of electric charge. ...

However, a charge build up 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.) See Capacitor (component) for a discussion of specific types. ... Displacement current is a quantity related to changing electric field. ...

More technically, Kirchhoff's current law can be found by taking the divergence of Ampère'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. ... An electric current produces a magnetic field. ... In physics and mathematical analysis, Gausss law is the electrostatic application of the generalized Gausss theorem giving the equivalence relation between any flux, e. ...

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. This can also be interpreted as a special case of Gauss's law for a small point containing no electric charge. In physics and mathematical analysis, Gausss law is the electrostatic application of the generalized Gausss theorem giving the equivalence relation between any flux, e. ...

A matrix version of Kirchhoff's current law is the basis of most circuit simulation software, such as SPICE or NI Multisim. For other uses, see Spice (disambiguation). ... NI Multisim, formerly known as MultiSIM, is an electronic schematic capture and simulation program which employs Berkeleys SPICE based software simulation. ...

Kirchhoff's Voltage Law (KVL)

The sum of all the voltages around the loop is equal to zero. v₁ + v₂ + v₃ + v₄ = 0

This law is also called Kirchhoff's second law, Kirchhoff's loop rule, and Kirchhoff's second rule. It is a consequence of the principle of conservation of energy. Image File history File links Kirchoffs Voltage Law File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... In physics, the conservation of energy states that the total amount of energy in an isolated system remains constant, although it may change forms, e. ...

The principle of conservation of energy implies that:

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

(Otherwise, it would be possible to build a perpetual motion machine that passed a current in a circle around the circuit.) Potential difference is a quantity in physics related to the amount of energy that would be required to move an object from one place to another against various types of force. ... 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). ...

Considering that electric potential is defined as line integral of electric field, Kirchhoff's voltage law can be expressed equivalently with equation This article does not cite any references or sources. ... This article is about path integrals in the general mathematical sense, and not the path integral formulation of physics which was studied by Richard Feynman. ... In physics, the space surrounding an electric charge or in the presence of a time-varying magnetic field has a property called an electric field. ...

which states that line integral of electric field around closed loop C is zero. This article is about path integrals in the general mathematical sense, and not the path integral formulation of physics which was studied by Richard Feynman. ... In physics, the space surrounding an electric charge or in the presence of a time-varying magnetic field has a property called an electric field. ...

This is a simplification of Faraday's law of induction for the special case where there is no fluctuating magnetic field linking the closed loop. 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. This is because energy is being transferred from the magnetic field to the current (or vice versa). In order to "fix" Kirchhoff's voltage law for circuits containing inductors, an effective potential drop, or electromotive force (emf), is associated with each 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. Faradays law of induction (more generally, the law of electromagnetic induction) states that the induced emf (electromotive force) in a closed loop equals the negative of the time rate of change of magnetic flux through the loop. ... Magnetic field lines shown by iron filings In physics, the space surrounding moving electric charges, changing electric fields and magnetic dipoles contains a magnetic field. ... In physics, the space surrounding an electric charge or in the presence of a time-varying magnetic field has a property called an electric field. ... In physics, the conservation of energy states that the total amount of energy in an isolated system remains constant, although it may change forms, e. ... In physics, a potential may refer to the scalar potential or to the vector potential. ... This article is about path integrals in the general mathematical sense, and not the path integral formulation of physics which was studied by Richard Feynman. ... Electromotive force (emf) is the amount of energy gained per unit charge that passes through a device in the opposite direction to the electric field existing across that device. ... An electric current i flowing around a circuit produces a magnetic field and hence a magnetic flux Φ through the circuit. ... Faradays law of induction (more generally, the law of electromagnetic induction) states that the induced emf (electromotive force) in a closed loop equals the negative of the time rate of change of magnetic flux through the loop. ...

See also

Electronics Portal

• Kirchhoff's law of thermal radiation
• Faraday's law of induction
• Gauss's law
• Maxwell's equations
• Conservation of energy
• SPICE (Simulation Program with Integrated Circuits Emphasis)

KVL may also be stated as " the algebraic sum of various potential drops across an electrical circuit is equal to the electromotive force acting on the circuit" Image File history File links Nuvola_apps_ksim. ... Kirchhoffs law in thermodynamics, also called e. ... Faradays law of induction (more generally, the law of electromagnetic induction) states that the induced emf (electromotive force) in a closed loop equals the negative of the time rate of change of magnetic flux through the loop. ... In physics and mathematical analysis, Gausss law is the electrostatic application of the generalized Gausss theorem giving the equivalence relation between any flux, e. ... For thermodynamic relations, see Maxwell relations. ... In physics, the conservation of energy states that the total amount of energy in an isolated system remains constant, although it may change forms, e. ... For other uses, see Spice (disambiguation). ... Integrated circuit of Atmel Diopsis 740 System on Chip showing memory blocks, logic and input/output pads around the periphery Microchips with a transparent window, showing the integrated circuit inside. ...

References

• Paul, Clayton R. (2001). Fundamentals of Electric Circuit Analysis. John Wiley & Sons. ISBN 0-471-37195-5. 
• Serway, Raymond A.; Jewett, John W. (2004). Physics for Scientists and Engineers (6th ed.). Brooks/Cole. ISBN 0-534-40842-7. 
• Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8. 

External links

• http://www.sasked.gov.sk.ca/docs/physics/u3c13phy.html