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

c. The capacity reactance, or

		1		1
Xc	=		=		=	72.4 ohms
		2πfC		2 × 3.1416 × 100 × .000022

(note that 22 microfarads are reduced to .000022 farad before substituting in the formula. Why? See page [1,042]).

Substituting values as calculated in equation (3), page [1,060].

Z = √(4² + (94.2 - 72.4)²) = √(491) = 22.2 ohms.

Fig. 1,303.—Diagram of a resonant circuit. A circuit is said to be resonant when the inductance and capacity are in such proportion that the one neutralizes the other, the circuit then acting as though it contained only resistance. In the above circuit X_i = 2πfL = 2 × 3.1416 × 100 × .01 = 6.28 ohms; X_c = 1 ÷ (2 × 3.1416 × 100 × .000253) = 6.28 ohms whence the resultant reactance = X_i - X_c = 6.28 - 6.28 = 0 ohms. Z = √(R² + (X_i - X_c)²) = √(7² + 0²) = 7 ohms.

Ques. Why is capacity reactance given a negative sign?

Ans. Because it reacts in opposition to inductance, that is it tends to reduce the spurious resistance due to inductance.

In circuits having both inductance and capacity, the tangent of the angle of lag or lead as the case may be is the algebraic sum of the two reactances divided by resistance. If the sign be positive, it is an angle of lag; if negative, of lead.