. K IRCHHOFF ’ S R ULES Electric circuits generally consist of a number of resistors and cells interconnected sometimes in a complicated way. The formulae we have derived earlier for series and parallel combinations of resistors are not always sufficient to determine all the currents and potential differences in the circuit. Two rules, called Kirchhoff’s rules , are very useful for analysis of electric circuits.
Given a circuit, we start by labelling currents in each resistor by a symbol, say I , and a directed arrow to indicate that a current I flows along the resistor in the direction indicated. If ultimately I is determined to be positive, the actual current in the resistor is in the direction of the arrow. If I turns out to be negative, the current actually flows in a direction opposite to the arrow. Similarly, for each source (i.e., cell or some other source of electrical power) the positive and negative electrodes are labelled as well as a directed arrow with a symbol for the current flowing through the cell.
This will tell us the potential difference, V = V (P) – V (N) = ε – I r Gustav Robert Kirchhoff ( – ) German physicist, professor at Heidelberg and at Berlin. Mainly known for his development of spectroscopy, he also made many important contributions to mathe- matical physics, among them, his first and second rules for circuits.