The paper presents a generalization of Ramo's theorem to conducting media. The generalized reciprocity theorem derived here is valid for configurations consisting of N metallic electrodes of arbitrary shape embedded in any conducting or non-conducting medium, and, furthermore, holds for non-shorted electrodes and for arbitrarily large signals. Its generality makes the theorem potentially applicable in many different areas concerned with measurement, registration, and interpretation of distributions of current in a variety of electronic media such as vacuum, plasmas, electrolytes, biological tissue, semiconductors, and many others. As an example of a typical application the latter part of the paper shows how the generalized theorem can be used for analysis of excessive flicker noise in semiconductors. In this analysis the noise properties of N-terminal devices are described, in particular the dependence of excessive noise on typical semiconductor parameters and geometrical structure.