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Home Fundamentals A.C. Circuits Reactance and Impedance  
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Reactance and ImpedanceAuthor: J.B. Hoag
The opposition which a pure inductance (an inductor without resistance or capacitance) offers to the flow of an alternating current is called its inductive reactance and is represented by X_{L}. It will be greater, the greater the inductance L (henries) and the higher the frequency f (cycles per second), and in direct proportion in both cases. Thus X_{L} = 2πfL (ohms). The opposition to the flow of alternating current which is set up by a pure condenser (capacitor without resistance or inductance) is called capacitative reactance and is represented by X_{L}. The greater the capacitance C (farads) and/or the greater the frequency f (cycles per second), the less X_{c} will be. Thus
The opposing effect of a capacitance and an inductance connected together one after the other (in series) is called the total reactance, X, of the circuit. It is given by: X = X_{L}  X_{c} (ohms). The inductive reactance is taken as positive. The total opposition to alternating current flow, set up by a pure resistance, inductance, and capacitance in series with each other, is called the impedance of the circuit and is given by
It is to be noted that R and X are not added algebraically but as though they were at right angles to each other. Ohm's law for an a.c. circuit is: E = IZ, as contrasted with E = IR for a d.c. circuit. The currents I (r.m.s. values) which flow under the conditions discussed above are shown graphically in Fig. 5 A, where the frequency of the oscillator is raised from zero (d.c.) to higher and higher values.
Comparative reactances are given in Table 5 A and should be examined carefully by the student.


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