=293. Heat Developed in a Conductor.=--A rule for computing the amount of heat produced in an electric circuit by a given current has been accurately determined by experiment. It has been found that 1 _calorie_ of heat (Art. 142), is produced by an expenditure of 4.2 joules of electrical (or other) energy. In other words, 1 joule will produce 1/4.2 or 0.24 calorie. Now the number of joules of electrical energy in an electric circuit is expressed by the following formula: Joules = volts × amperes × seconds, or since 1 joule = 0.24 calorie, Calories = volts × amperes × seconds × 0.24 or _H_ = _EI_ × _t_ × 0.24 (1) By Ohm's law, _I_ = _E_/_R_ or _E_ = _I_ × _R_, substituting in equation (1) _IR_ for its equal _E_ we have _H_ = _I²R_ × _t_ × 0.24 (2) Also since _I_ = _E_/_R_ substitute _E_/_R_ for _I_ in equation (1) and we have _H_ = _E²_/_R_ _t_ × 0.24 (3) To illustrate the use of these formulas by a problem suppose that a current of 10 amperes is flowing in a circuit having a resistance of 11 ohms, for 1 minute. The heat produced will be by formula (2) = (10)² × 11 × 60 × 0.24 equals 15,840 calories. [Illustration: FIG. 273.--A carbon filament incandescent lamp.] [Illustration: FIG. 274.--A tungsten lamp.] =294. The Incandescent Lamp.=--One of the most common devices employing the heat effect of an electric current is the _incandescent lamp_. (See Fig. 273.) In this lamp the current is sent through a carbon filament, which is heated to incandescence. In order to keep the filament from burning as well as to prevent loss of heat by convection, it is placed in a glass bulb from which the air is exhausted. Two platinum wires fused in the glass connect the carbon filament with the grooved rim and the end piece of the base. The end piece and rim connect with the socket so that an electric current may flow through the filament of the lamp. The carbon incandescent lamp has a low efficiency. It takes 0.5 ampere of current at 110 volts or in other words it requires 55 watts to cause a 16-candle-power lamp to glow brightly, hence 1 candle power in this lamp takes 55/16 = 3.43 watts. The _efficiency of electric lamps_ is measured by the _number of watts per candle power_. This is a peculiar use of the term efficiency, as the larger the number the less efficient is the lamp. More efficient lamps have been devised with filaments of the metals _tantalum_ and _tungsten_ (Fig. 274). These give a whiter light than do carbon lamps, and consume but about 1.25 watts per candle power. COMPARATIVE "EFFICIENCY" OF ELECTRIC LAMPS