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SelfInductanceSelfinductance is defined^{1} as "the (scalar) property of an electric circuit which determines, for a given rate of change of current in the circuit, the electromotive force induced in the same circuit. Thus
where e_{1} and i_{1} are in the same circuit, and L is the coefficient of selfinductance.'' In this equation e_{1} is the instantaneous induced electromotive force in volts, L is the selfinductance in henrys, and di_{1}/dt is the instantaneous rate of change of current in amperes per second. The magnitude of the instantaneous induced electromotive force is e_{1} = N dφ_{1}/10^{8}dt. If this is substituted in equation 2, the magnitude of the selfinductance becomes
Communication equipment such as coils and transformers often have closed cores of ferromagnetic material. Also, coils sometimes have directcurrent and alternatingcurrent components flowing simultaneously in the windings. The inductance of such units can be found by equation 3, assuming that the magnetic characteristics of the material are known. This is shown by Fig. 1 which illustrates the way in which the magnetic flux φ varies in a ferromagnetic core with the current i_{1} that produces it. Suppose that the value of the directcurrent components is i_{1}' and that the alternatingcurrent component is as shown by Δi_{1}'; then, the corresponding flux change will be Δφ'. Hence, dφ_{1}/di_{1} of equation 3 will have a certain value, and the selfinductance L a certain magnitude. Now suppose that the value of the directcurrent component i_{1}'' is different from i_{1}', being larger as shown in Fig. 1. The same change in current Δi_{1}" now produces but a very small change in magnetic flux Δφ", and hence dφ_{1}/di_{1} of equation 3 will be very small and the inductance will be much less than when the directcurrent component is at i_{1}'. Because of these variations, the inductance of a coil on a ferromagnetic core is called the incremental selfinductance, or merely incremental inductance. This may be regarded as a nonlinear selfinductance.
For coils and transformers with air cores, or ferromagnetic cores containing large air gaps, the inductance can be found by equation 3, or by the simplified form
In such equipment the inductance is essentially independent of the magnitude of the current. The flux φ_{1} produced by current i_{1} is found by the usual methods. The selfinductance L will be in henrys when N is the number of turns, φ_{1} is in lines, and i_{1} is the current in amperes. This may be regarded as a linear selfinductance. Sometimes inductance is measured with ordinary alternatingcurrent measuring instruments that indicate effective values. For steadystate sinusoidal conditions and effective values, equation 3 becomes
In these equations E_{L} is the magnitude of the effective value of the voltage drop in volts caused by the inductive reactance (excluding that caused by the effective resistance), I is the magnitude of the effective value of current in amperes, and f is the frequency in cycles per second. Such a determination would necessitate the use of a voltmeter, an ammeter, and a wattmeter to find the effective resistance or powerfactor angle so that the reactive voltage drop E_{L} could be separated from the total voltage drop across the circuit or coil. The voltage E_{L }leads the current I by 90°. If the coil saturates and if the impressed voltage is sinusoidal, the current will be distorted and will contain harmonics. In this event, the ammeter will read the effective value of the current, and equation 5 will give effective selfinductance. A discussion of inductance when iron is present is given in reference 2,


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