Resonance.—The effects of inductance and capacity, as already explained, oppose each other. If inductance and capacity be present in a circuit in such proportion that the effect of one neutralizes that of the other, the circuit acts as though it were purely non-inductive and is said to be in a state of resonance.
For instance, in a circuit containing resistance, inductance, and capacity, if the resistance be, say, 8 ohms, the inductance 30, and the capacity 30, then the impedance is
√(82 + (302 - 302)) = √(82) = 8 ohms.
Fig. 1,304.—Application of a choking coil to a lighting circuit. The coil is divided into sections with leads running to contacts similar to a rheostat. Each lamp is provided with an automatic short-circuiting cutout, and should one, two, or more of them fail, a corresponding number of sections of the choking apparatus is put in circuit to take the place of the broken lamp or lamps, and thus keep the current constant. It must not be supposed that this arrangement of lamps, etc. is a general one; it being adopted to suit certain special conditions.
The formula for inductance reactance is Xi = 2πfL, and for capacity reactance, Xc = 1 ÷ (2πfC); accordingly if capacity and inductance in a circuit be equal, that is, if the circuit be resonant
| 1 | |||
| 2πfL | = | (1) | |
| 2πfC |
from which
| 1 | |||
| f | = | (2) | |
| 2π√(CL) |