Electrical measurementsA laboratory manual . - R^i^ = MJ- ^dt = 0, and 31,J = Rjhdt; MyJ= ^t, Therefore M^_Ri fhdtM:^~Rs Jhdt But since there is no integrated current through thegalvanometer ^fhdt. Hence —^ = -—^ M^ R, After a balance has been obtained the resistances Ri,Rg may be measured by means of a Wheatstones is assumed in this discussion that Li and X3 are bothconstants. 124. Modification of Maxwells Method of coni-paring Mutual Inductances. — Let the resistance, self^induction, and current through coil ^1 (Fig. 125),including the galvanometer, be represented by i
Electrical measurementsA laboratory manual . - R^i^ = MJ- ^dt = 0, and 31,J = Rjhdt; MyJ= ^t, Therefore M^_Ri fhdtM:^~Rs Jhdt But since there is no integrated current through thegalvanometer ^fhdt. Hence —^ = -—^ M^ R, After a balance has been obtained the resistances Ri,Rg may be measured by means of a Wheatstones is assumed in this discussion that Li and X3 are bothconstants. 124. Modification of Maxwells Method of coni-paring Mutual Inductances. — Let the resistance, self^induction, and current through coil ^1 (Fig. 125),including the galvanometer, be represented by i?i, Xi,ii, respectively; and let the same quantities for the coilJ-sbe denoted by R-, Xo, and 4. The resistances are to SELF-IXDUCTIOW AND MUTUAL INDUCTION z6 i be varied till the galvanometer shows no deflection onworking the keyK. Let the cur-rents through ^^2and Ai be 4 andii and their finalsteady values I2and li. Let H bethe resistance ofthe branch AB^and S that of PQ. When the currents in A2 and A^^ have reachedtheir steady value. Fig 125. Ii=l2 R + R2 Express the potential difference between P and Q by thethree paths for any instant, and place their values equalto one another. Then dt dt B^^ = M, It dt Sii— jSi^ The electromotive force by the JLg branch is arranged tobe opposed to that of the Ai branch. Integrate from ^ = 0 to t = T when the steady statehas been attained in the battery circuit, and M,Jo - LJdir - RJixdt = M,J, - LJdisS/hdt - Sf{,dt. RJhdt = But Lifdii, Rifiidt^ L-^fdi^^ Sfiidt are all zero when abalance has been obtained, or when the galvanometershows no integrated current through it when the circuitis opened or closed, or on reversing if the double commu-tator is used. Since the current is zero when t — 0 and 268 ELECTRICAL MEASUREMENTS. when t — T, the sum of the increments dii equals thatof the decrements — dii. Also the galvanometer showsthe integrated current Il to be zero. So also the integralydis is zero because 4 is zero both when t
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