Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/389

 

a third method. Beginning with an arrangement in which the transient current due to self-induction is slightly in excess of that due to mutual induction, we may get rid of the inequality by inserting a conductor whose resistance is $W$ between $A$ and $Z$. The condition of no permanent current through the galvanometer is not affected by the introduction of $W$. We may therefore get rid of the transient current by adjusting the resistance of $W$ alone. When this is done the value of $L$ is

$L=-\left(1+{\frac {P}{Q}}+{\frac {P+R}{W}}\right)M$.

(15)

Comparison of the Coefficients of Self-induction of Two Coils.

757.] Insert the coils in two adjacent branches of Wheatstone's Bridge. Let $L$ and $N$ be the coefficients of self-induction of the coils inserted in $P$ and in $R$ respectively, then the condition of no galvanometer current is

$\left(Px+L{\frac {dx}{dt}}\right)Sy=Qy\left(Rx+N{\frac {dx}{dt}}\right)$,

(16)

whence

$PS=QR$,⁠ for no permanent current,

(17)

and

${\frac {L}{P}}={\frac {N}{R}}$, for no transient current.

(18)

Hence, by a proper adjustment of the resistances, both the permanent and the transient current can be got rid of, and then the ratio of $L$ to $N$ can be determined by a comparison of the resistances.