FIG. 1.
(b.) The internal opposition arises from the resistance, R, the capacity, K, and the electromagnetic inertia, L, of the circuit. A current of electricity takes time to rise to its maximum strength and time to fall back again to zero. Every circuit has what is called its time constant, t, Fig. 1, which regulates the number of current waves which can be transmitted through it per second. This is the time the current takes to rise from zero to its working maximum, and the time it takes to fall from this maximum to zero again, shown by the shaded portions of the figure; the duration of the working current being immaterial, and shown by the unshaded portion.
The most rapid form of quick telegraphy requires about 150 currents per second, currents each of which must rise and fall in 1/150 of a second, but for ordinary telephone speaking we must have about 1,500 currents per second, or the time which each current rises from zero to its maximum intensity must not exceed 1/3000 part of a second. The time constant of a telephone circuit should therefore not be less than 0.0003 second.
Resistance alone does not affect the time constant. It diminishes the intensity or strength of the currents only; but resistance, combined with electromagnetic inertia and with capacity, has a serious retarding effect on the rate of rise and fall of the currents. They increase the time constant and introduce a slowness which may be called retardance, for they diminish the rate at which currents can be transmitted. Now the retardance due to electromagnetic inertia increases directly with the amount of electromagnetic inertia present, but it diminishes with the amount of resistance of the conductor. It is expressed by the ratio L/R while that due to capacity increases directly, both with the capacity and with the resistance, and it is expressed by the product, K R. The whole retardance, and, therefore, the speed of working the circuit or the clearness of speech, is given, by the equation
(L / R ) + K R = t
or
L + K R² = R t
Now in telegraphy we are not able altogether to eliminate L, but we can counteract it, and if we can make Rt = Q, then
L = - K R²