Gustav Robert Kirchhoff
born March 12, 1824, Königsberg, Prussia [now Kaliningrad, Russia]
died Oct. 17, 1887, Berlin, Germany

Kirchhoff was one of the foremost physicists of the 19th century and is remembered as one of the founders of the science of spectroscopy. He is also known for Kirchhoff's laws, formulated in 1845 while he was still a student, which refer to the currents and electromotive forces in electrical networks.


Gustav Kirchhoff was born in Königsberg, Prussia. He was the son of a lawyer. When little he was talkative, and rather small for his age, and fragile by appearance. He went to University at the age of 18 to read math. He was influenced by the physicist Franz Neumann. Gustav Kirchhoff was also a student of Gauss. His first published paper won him a prize, and a place on the Berlin Physicists Society. He enjoyed a great social life, and worried that others would think him lazy. He published a paper on straight and circular conductors, and this formed his thesis.

In 1845 Kirchhoff first announced Kirchhoff's laws, which allow calculation of the currents, voltages, and resistances of electrical networks. Extending the theory of the German physicist Georg Simon Ohm, he generalized the equations describing current flow to the case of electrical conductors in three dimensions. In further studies he demonstrated that current flows through a conductor at the speed of light. He was a physicist who made important contributions to the theory of circuits using topology and to elasticity. Kirchhoff's laws, finally announced in 1854, allow calculation of currents, voltages and resistances of electrical circuits extending the work of Ohm. In 1857, he worked on conduction in telegraph wires. He discovered that the velocity of transmission is the same as the speed of light.

Kirchhoff's circuit rules named after Gustav Robert Kirchhofft are two statements about multi-loop electric circuits that embody the laws of conservation of electric charge and energy and that are used to determine the value of the electric current in each branch of the circuit.
Kirchoff's Current Law

The first rule, the junction theorem, states that the sum of the currents into a specific junction in the circuit equals the sum of the currents out of the same junction. Electric charge is conserved: it does not suddenly appear or disappear; it does not pile up at one point and thin out at another.

Stated another way

No matter how many paths into and out of a single point all the current leaving that point must equal the current arriving at that point.

Kirchhoff's Voltage Law

The second rule, the loop equation, states that around each loop in an electric circuit the sum of the emf 's (electromotive forces, or voltages, of energy sources such as batteries and generators) is equal to the sum of the potential drops, or voltages across each of the resistances, in the same loop. All the energy imparted by the energy sources to the charged particles that carry the current is just equivalent to that lost by the charge carriers in useful work and heat dissipation around each loop of the circuit.

Stated another way:

The voltage drops around any closed loop must equal the applied voltages.

On the basis of Kirchhoff's two circuit rules, a sufficient number of equations can be written involving each of the currents so that their values may be determined by an algebraic solution. Kirchhoff's circuit rules are also applicable to complex alternating-current circuits and with modifications to complex magnetic circuits.

In 1847 Kirchhoff became Privatdozent (unsalaried lecturer) at the University of Berlin and three years later, in 1950, he accepted the post of extraordinary professor of physics at the University of Breslau. In 1851 Robert Bunsen joined the university as professor of chemistry and formed a friendship with Kirchhoff. Their friendship and scientific cooperation resulted in very important scientific achievements. Bunsen was called to the University of Heidelberg in 1852, and he soon arranged for Kirchoff to teach at Heidelberg as well.


Gustav Robert Kirchoff (left) and
Robert Wilhelm Eberhard Bunsen

In 1854 Kirchhoff was appointed professor of physics at the University of Heidelberg, where he joined forces with Bunsen and founded spectrum analysis. Bunsen was analyzing the colors given off by heating chemicals to incandescence, using colored glass to distinguish between similar shades. Kirchhoff joined this research when he suggested that the observation of spectral lines, by dispersing the light with a prism, would be a more precise way of testing the color of the light. Kirchhoff and Bunsen found that each substance emitted light that had its own unique pattern of spectral lines - a discovery that began the spectroscopic method of chemical analysis. In 1860, a few months after publishing these results, they discovered a new metal, which they called cesium, and the next year (1861) found rubidium. Kirchhoff and Bunsen also constructed improved forms of the spectroscope for such work.

These discoveries inaugurated a new era in the means used to find new elements. The first fifty elements discovered — beyond those known since ancient times — were either the products of chemical reactions or were released by electrolysis. From 1860 the search was on for trace elements detectable only with the help of specialized instruments like the spectroscope.

Bunsen-Kirchoff spectroscope with the Bunsen burner
(labeled D) from Annalen der Physik (1860)

Kirchhoff and Bunsen began by effectively inventing the spectroscope, a prism-based device that separated light in its primary chromatic components, i.e., its spectrum, with which they began studying the spectral "signature" of various chemical elements in gaseous form.

In 1856 Gustav Kirchhoff  met his future wife, Clara, 14 years younger than him.

Kirchhoff went further to apply spectrum analysis to study the composition of the Sun. He discovered the sodium spectra in stars. He realised that the spectra of stars could be used to work out what is present in the stars. Kirchhoff was the first to explain the dark lines in the Sun's spectrum as caused by absorption of particular wavelengths as the light passes through a gas. He found that when light passes through a gas, the gas absorbs those wavelengths that it would emit if heated.

In 1859 he published an explanation of the dark lines in the solar spectrum discovered by Josef von Fraunhofer (Fraunhofer lines), in which he suggested that they are due to absorption of certain wavelengths by substances in the Sun's atmosphere. That discovery marked the beginning of a new era in astronomy.

He later formulated Kirchhoff's law of radiation, which concerns the emission and absorption of radiation by a hot body. It states that the rate of emission of energy by a body is equal to the rate at which the body absorbs energy (both emission and absorption being in a given direction at a given wavelength). Kirchhoff gave a final proof of this in 1861. His work on black body radiation was fundamental in the development of quantum theory.

Kirchhoff was crippled by an accident in mid-life but remained in good spirits and, when his health forced him to stop experimental work in 1875, he was offered the chair of theoretical physics at the University of Berlin. Disability meant he had to spend much of his life on crutches or in a wheelchair. His best known works are the four volume masterpiece "Vorlesungen über mathematische Physik" (1876-94, "Lectures on Mathematical Physics") and "Gesammelte Abhandlungen" (1882; supplement, 1891, "Collected Essays"). In 1881 he was elected to the Electrical Congress in Paris, as the German delegate. His failing health forced him to prematurely retire in 1886.

Gustav Robert Kirchhoff died in Berlin on 17 October 1887.

Kirchhoff was memorized in German stamps. His work in electricity is noted on the stamp shown at right: the sum of potential drops around a closed circuit loop is zero.