46CHAPTER 2. OHM’S LAWIf,I=ERandP = I EThen,P =orP =R2II R()IA historical note: it was James Prescott Joule, not Georg Simon Ohm, who ﬁrst discoveredthe mathematical relationship between power dissipation and current through a resistance.This discovery, published in 1841, followed the form of the last equation (P = I2R), and isproperly known as Joule’s Law. However, these power equations are so commonly associatedwith the Ohm’s Law equations relating voltage, current, and resistance (E=IR ; I=E/R ; andR=E/I) that they are frequently credited to Ohm.P = IEP =P =ERE2I2RPower equations• REVIEW:• Power measured in watts, symbolized by the letter ”W”.• Joule’s Law: P = I2R ; P = IE ; P = E2/R2.5ResistorsBecause the relationship between voltage, current, and resistance in any circuit is so regular,we can reliably control any variable in a circuit simply by controlling the other two. Perhapsthe easiest variable in any circuit to control is its resistance. This can be done by changing thematerial, size, and shape of its conductive components (remember how the thin metal ﬁlamentof a lamp created more electrical resistance than a thick wire?).Special components called resistorsare made for the express purpose of creating a precisequantity of resistance for insertion into a circuit. They are typically constructed of metal wireor carbon, and engineered to maintain a stable resistance value over a wide range of environ-mental conditions. Unlike lamps, they do not produce light, but they do produce heat as electricpower is dissipated by them in a working circuit. Typically, though, the purpose of a resistor isnot to produce usable heat, but simply to provide a precise quantity of electrical resistance.The most common schematic symbol for a resistor is a zig-zag line:Resistor values in ohms are usually shown as an adjacent number, and if several resistorsare present in a circuit, they will be labeled with a unique identiﬁer number such as R1, R2,R3, etc. As you can see, resistor symbols can be shown either horizontally or vertically: