I
EXPERIMENTS TO DETERMINE AN UPPER LIMIT
TO THE KINETIC ENERGY OF AN ELECTRIC
CURRENT.
(Wiedemann's Annalen, 10, pp. 414-448, 1880.)
ACCORDING to the laws of induction the current i in a
linear circuit, in which a variable electromotive force A acts,
is given by its initial value together with the differential
equation
ir = A P
-
di
dt'
where is the resistance and P the inductance of the circuit.¹
Multiplying by idt we get the equation
Aidt i²rdt+d(Pi²),
=
which shows that the law expressed by the above equation is
in agreement with the principle of the conservation of energy
on the assumption that the work done by the battery on the
one hand, and the heat developed in the circuit and the
increase of potential energy on the other hand, are the only
amounts of energy to be considered. This supposition is not
true, and hence the above equations cannot lay claim to
complete accuracy, in case the electricity in motion possesses
inertia, the effect of which is not quite negligible. In this
case we must add to the right-hand side of the second equation
1 [The notation has been altered in accordance with English custom and
the necessary changes in the equations made. The original has 2P.-TR.]
M.P.
B