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

Z = X_i - X_c = 18.85 - 10 = 8.85 ohms

When a circuit contains besides resistance, both inductance and capacity, the formula for impedance as given in equation (1), page [1,058], must be modified to include the reactance due to capacity, because, as explained, inductive and capacity reactances work in opposition to each other, in the sense that the reactance of inductance acts in direct proportion to the quantity 2πfL, and the reactance of capacity in inverse proportion to the quantity 2πfC. The net reactance due to both, when both are in the circuit, is obtained by subtracting one from the other.

Fig. 1,300.—Diagram of circuit for example IV.

To properly estimate impedance then, in such circuits, the following equation is used:

impedance = √(resistance² + (inductance reactance - capacity reactance)²)

or using symbols,

Z = √(R² + (X_i - X_c)²) (3)

EXAMPLE IV.—A current has a frequency of 100. It passes through a circuit of 4 ohms resistance, of 150 milli-henrys inductance, and of 22 microfarads capacity. What is the impedance?