Electrical Engineering ⇒ Topic : Expressions for Selfinductance

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Expressions for Selfinductance The selfinductance (L) of a circuit or coil can be determined by one of the following three ways : (1) First Method. If the magnitude of selfinduced e.m.f. (e) and the rate of change of current (dI/dt) are known, then inductance can be determined from the following relation :
(2) Second Method. If the flux linkages of the coil and current are known, then inductance can be determined as under : Thus, inductance is the flux linkages of the coil per ampere. If N 4) = 1 Wbturn and I = 1 A, then L= 1H. Hence a coil has an inductance of 1 henry if a current of 1 A in the coil sets up flux linkages of 1 Whturn. Note. Relation (ii) above reveals that inductance depends upon the ratio O/I. Therefore, inductance is constant only when the flux changes uniformly with current. This condition is met only when the flux path is entirely composed of nonmagnetic material e.g. air. But when the flux path is through a magnetic material ( e.g. coil wound over iron bar), inductance of the coil will be constant only over the linear portion of the magnetisation curve. (3) Third Method. The inductance of a magnetic circuit can be found in terms of its physical dimensions. Consider an ironcored *solenoid of dimensions as shown in Fig. (a) Inductance of the solenoid is given by [from exp. (ii) above]
figure (a) ........... (iii) Thus, inductance can be determined by using the relation (iii) or (iv). It is important to note [See relation (iv)] that inductance is directly proportional to turns squared and inversely proportional to the reluctance of the magnetic path. The smaller the reluctance of the magnetic path, the larger the inductance and viceversa. For this reason, an ironcored coil has more inductance than the equivalent aircored coil  
 
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