By Frederick W. Grover
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Extra resources for Inductance Calculations. Working formulas and tables.
Sample text
3862 50 CALCULATION OF MUTUAL INDUCTANCE AND SELF-INDUCTANCE the mutually induced emfs would act with the self-induced emfs and in the other would oppose them. AB E becomes smaller, they forro a "retum" circuit; the mutual inductance makes the total inductance of the combination less than the sum of their self-inductances, so that in the general formula applicable to a return circuit, L = L1 + L 2 - 2M12 , the mutual inductance is to be taken as a positive quantity. However, if the angle E is obtuse, the series combination has a greater total inductance than the sum of the self-inductances and M 12 is to be considered as a negative quantity in the general equation, so as to give L = L 1 + L 2 + 2M12 .
Minor, b = ~ . Then, since for {Ja. b 'Y = 65 Inductance of Circuits Enclosing Plane Curves. Circuits of wire bent so as to enclose oval areas and the like may be readily treated by the Bashenoff method. From the plotted curve may be found by planimeter or other instruments the perimeter and enclosed area. From these may be calculated the ratio l/y'S. If this has a value less than 4, the value of cJ, may be interpolated from the curve for regular polygons. If the ratio is greater, the value may be obtained from the ~urve for r~ctangles.
1 ........ , ~ 1 the lengths l and m, the distances µ. and " and the )", 1 angle e, or, instead, the measured values of the ' 1 ', 1 four distances R 1 , R2 , R 3 , and R4 may be specified. ' The equations connecting the two systems are Fio. 001 [<µ. + l) tanh- 1 - m2) + a 2(R22 - R3 2 - Z2)Jm 4z2,n2 - ª4 ' + Z) 2 + (11 + m) 2 - 2(µ. + l)(v + m) cos E, R2 2 = (µ. + l) 2 + 112 - 2v(µ. + l) cos E, R 3 2 = µ. 11 cos E, R 4 2 = µ. (v + m) cos E. µ. + (11 + m) tanh- 1 m R1 E - + R2 tanh-1 m R3 + R4 - 11 l + R4 R1 tanh- 1 l R2 + Ra ] , (50) the subscripts denoting the lengths of the filaments entering into each term, it will be seen that each of the four terms in (51) is the mutual inductance of two filaments meeting at a point and may be calculated by (45) using Table 7.