Electrical measurementsA laboratory manual . edle of the tangent galvanometer dependsupon the magnetic field due to the coil at the several positions ofthe needle. The tangents of the deflections therefore follow thesame law of variation as that of the mutual inductance at differentdistances. 126. To compare the Mutual Inductance of TwoCoils with the Self-Inductance of One of Them.^ —Let the coil of resistance By and self-inductance L bemcluded in one branch ^6 of a Wheatstones bridge(Fig. 128) whose other branches are other coil of the pair is put in the battery branch, and
Electrical measurementsA laboratory manual . edle of the tangent galvanometer dependsupon the magnetic field due to the coil at the several positions ofthe needle. The tangents of the deflections therefore follow thesame law of variation as that of the mutual inductance at differentdistances. 126. To compare the Mutual Inductance of TwoCoils with the Self-Inductance of One of Them.^ —Let the coil of resistance By and self-inductance L bemcluded in one branch ^6 of a Wheatstones bridge(Fig. 128) whose other branches are other coil of the pair is put in the battery branch, and is so connectedthat the currentflows in oppositedirections throughthe two coils. Theself-inductance ofthe coil P thereforeproduces an electro-motive force oppo-site in direction tothat due to the mu-tual induction M be-tween P and Q, and the one may be made to balancethe other. The resistances Ri, Bi, B^, and B^ are to be adjustedtill there is a balance for steady currents. Then we mayget rid of transient currents through the galvanometer. Fig. 128. Maxwells Flee, and Mag., Vol. II., p. 365. SELF-INDUCTION AND MUTUAL INDUCTION. 273 by altering Ro and H^ in such a way that their ratioremains constant. There will then be neither transientnor permanent currents through the galvanometer. Let the current from A to C be h, and that from Ato 2), ?o. Then the current through Q will be ii + ^ potential difference between A and C will be dt \dt dtj ^ ^ The potential difference between A and D is i^s^.Since a balance is maintained between 6^ and D ?i^.,4 = i^,-. + i§-i^(f+ §). . (2) But if R>., i?3, and ^4 are inductionless resistances,I{42 = R\ii (3) Hence dt \dt dt) ^ ^ From (3) di^ _ Ri dii dt~^, dt Therefore from (4) L = m(i+ ^\, . (5) C ^ t) The double adjustment of R^ and i^4 may be avoided byjoining A and B by J?-. Beginning with an adjustmentin which the electromotive force due to self-induction isslightly in excess of that due to mutual induction, thelatter may be aug
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