An elementary book on electricity and magnetism and their applications . far we have been considering cir-cuits where the opposition to the flow of an alternating currentconsisted entirely of reactance and where the resistance wastoo small to be taken into account. Such is the case, however,only in such apparatus as the reactance coils used with light-ning arresters. In most electrical devices we have to considera combination of resistance and reactance, and therefore wespeak of the apparent resistance or impedance of a circuitthrough which an alternating current flows. The effective current i
An elementary book on electricity and magnetism and their applications . far we have been considering cir-cuits where the opposition to the flow of an alternating currentconsisted entirely of reactance and where the resistance wastoo small to be taken into account. Such is the case, however,only in such apparatus as the reactance coils used with light-ning arresters. In most electrical devices we have to considera combination of resistance and reactance, and therefore wespeak of the apparent resistance or impedance of a circuitthrough which an alternating current flows. The effective current in an alternating-current circuit is equalto the effective voltage applied to the circuit divided by the impedanceof the circuit. Current =Voltfge . Impedance It might be assumed that if we had a resistance of 3 ohmsand a reactance of 4 ohms the impedance would be the arith-metical sum; but experiment shows that the impedance is 5ohms. 330 ELECTRICITY AND MAGNETISM This is because we are dealing with a geometrical relation between the ohmic resistance and $Angle of Lag. Ohmic Resistance Fig. 226.—Ohmic resistanceand inductive resistance actat right angles. the inductive resistance. These two re-sistances are acting at right angles (90°)to each other. This is shown graphicallyin figure 226, in which the ohmic resistanceis represented by the horizontal line ACand the inductive resistance by the verti-cal line BC. The resultant resistance orthe impedance can be shown mathemati-cally to be represented by the hypothenuseAB of the right triangle. But we knowin a right triangle the square of the hy-pothenuse equals the sum of the squaresof the other two sides. That is, ~AB2 = AC2 + BC\ In general the square of the imped-ance equals the sum of the squares ofthe reactance and the resistance. Impedance = v Resistance2+reactance2. z=v/p+Ar» or, Z=Vi?2 + (2TT/L)2. Therefore for alternating currents in circuits containing re-sistance and inductance Ohms Law takes the form Voltage Current
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectmagnetism, bookyear19
