From Electromechanical Design Handbook, Third Edition
6.2 CIRCUIT ELEMENTS
6.2.1 Basic Circuit Formulas
Resistance in series:
Resistance in parallel:
Capacitance in series:
Capacitance in parallel:
The capacitance of a parallelplate capacitor element is given as

where C = capacitance, picofarads (pF)

K = dielectric constant of insulating medium

A = area of one plate, cm ^{2}

n = number of plates

d = thickness of the dielectric, cm
If A and d are given in inches, the constant (0.0885) becomes 0.224.
SelfInductance. In series:
In parallel:
Coupled Inductance. In series with fields aiding:
In series with fields opposing:
In parallel with fields aiding:
In parallel with fields opposing:

where L _{t} = total inductance

M = mutual inductance

L _{1}, L _{2} = selfinductance of individual coils
Mutual Inductance ( M)

where M = mutual inductance, same units as L _{A} and L _{O}

L _{A} = total inductance of coils L _{1} and L _{2}, fields aiding

L _{O} = total inductance of coils L _{1} and L _{2}, fields opposing
Resonance. The resonant frequency, or frequency at which inductive reactance ( X _{L}) equals capacitive reactance ( X _{C}) is given as

where f _{r} = resonant frequency, Hz

L = inductance, H

C = capacitance, F
Reactance. Inductive:
Capacitive:

where X _{L} = inductive reactance, ? (positive reactance)

X _{C}
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