EXAMPLE.—In a certain circuit the resistance is 4 ohms, and the reactance 3 ohms. What is the impedance?
In fig. 1,323, lay off, on any scale AB = 4 ohms and erect the perpendicular BC = 3 ohms. Join AC, which gives the impedance, and which is, measured with the same scale, 5 ohms.
EXAMPLE.—A coil of wire has a resistance of 20 ohms and an inductance of 15 milli-henrys. What is its impedance for a current having a frequency of 100?
Fig. 1,323.—Diagram for obtaining the impedance of a circuit containing 4 ohms resistance and 3 ohms reactance.
The ohmic value of the inductance, that is, the reactance is
2πfL = 2 × 3.1416 × 100 × .015 = 9.42 ohms.
In fig. 1,324, lay off, on any scale, AB = 20 ohms, and the perpendicular BC to length = 9.42 ohms. Join AC, which gives the impedance, which is, measured on the same scale, 22.1 ohms.
EXAMPLE.—What is the angle of lag in a circuit having a resistance of 4 ohms and a reactance of 3 ohms?
Construct the impedance diagram in the usual way as in fig. 1,325, then the angle included between the impedance and resistance lines (denoted by φ) is the angle of lag, that is, the angle BAC. By measurement with a protractor it is 37 degrees. By calculation the tangent of the angle of lag or