## EQUATIONS FOR SIMPLE R, 1, AND C NETWORKS*

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On: 07 Jul, 2017

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**Self-Inductance of Circular Ring of Round Wire at Radio Frequencies, for Nonmagnetic Materials **

*L = *(a/100) X [7.353 *log 10(16a/d) *— 6.386]

Where,

*L = *self-inductance in microhenrys,

*a = *mean radius of ring in inches,

*d = *diameter of wire in inches,

*aid> *2.5.

* Many equations for computing capacitance, inductance, and mutual inductance will be found in Bureau of Standards Circular No. C74, obtainable from the Superintendent of Documents, Government Printing Office, Washington, D.C. 20402.

**Capacitance **

*For Parallel-Plate Capacitor: *

where,

*C *0.0885€r[(N — *l)Ajit = *0.2256r[(N — 1)A”/t”]

*C = *capacitance in picofarads,

*A = *area of one side of one plate in square centimeters,

*A” = *area in square inches,

N *= *number of plates,

*= *thickness of dielectric in centimeters,

*= *thickness in inches,

*= *dielectric constant relative to air.

This equation neglects “fringing” at the edges of the plates.

*For Coaxial Cylindrical Capacitor *(Fig. 8):

*C *= *2TErE/[log(b/a)] *

= {(5 *x *106e)/[c2log(b/a)]}

where,

*C *= capacitance per unit axial length in farads/meter,

*c *velocity of light in vacuo, meters per second

= 2.998 X 108,

= dielectric constant relative to air,

= permittivity of free space in farads/meter

= 8.85 *x *10-12

Alternative forms of the equation are:

*C *= 0.241 66r/[log 10(b/a)J picofarads/centimeter = 0.6 l4E/[log *10(b/a)j *picofarads/inch = 7.36e,/[log *10(b/a)] *picofarads/foot

When 1.0 *< (b/a) *< 1.4, then with accuracy of 1 percent or better, the capacitance in picofarads/foot is:

*(b/a) + *

__1__

*C*= 8.5OEr

*(b/a)*—

**T-ir or V-A Transformation **

The two networks (Fig. 9) are equivalent, as far as conditions at the terminals are concerned, provided the listed equations are satisfied (either the impedance equations or the admittance equations may be used)

*Y1 *= 1/Z1 *Y *= *1/Zr, *etc.

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