Hawkins Electrical Guide v. 05 (of 10) / Questions, Answers, & Illustrations, A progressive course of study for engineers, electricians, students and those desiring to acquire a working knowledge of electricity and its applications

by N. Hawkins

Ques. If the capacity reactance be larger than the inductance reactance, how does this affect the sign of (X_i-X_c)²?

Ans. The sign of the resultant reactance of inductance and capacity will be negative if capacity be the greater, but since in the formula the reactance is squared, the sign will be positive.

Fig. 1,337.—Impedance diagram of a circuit containing 25 ohms resistance, 30 ohms inductance, and 40 ohms capacity. The resultant reactance being due to excess of capacity, the impedance line AC' falls below the horizontal line AB, indicating that the current leads pressure.

EXAMPLE.—What is the impedance in a circuit having 25 ohms resistance, 30 ohms inductance reactance, and 40 ohms capacity reactance?

To solve this problem graphically, draw the line AB, in fig. 1,337, equal to 25 ohms resistance, using any convenient scale.

At B draw upward at right angles BC = 30 ohms; draw from C downward CC' = 40 ohms. This gives -BC' (= BC - CC') showing the capacity reactance to be 10 ohms in excess of the inductance reactance. Such a circuit is equivalent to one having no inductance but the same resistance and 10 ohms capacity reactance.

The diagram is completed in the usual way by joining AC giving the required impedance, which by measurement is 26.9 ohms.

By calculation, Z = √(25² + (30 - 40)²) = √(25² + (-10)²) = 26.9.

Form of Impedance Equation without Ohmic Values.—