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# Resistance

Resistance is defined1 as "the (scalar) property of an electric circuit or of any body that may be used as a part of an electric circuit which determines for a given current the rate at which electric energy is converted into heat or radiant energy and which has a value such that the product of the resistance and the square of the current gives the rate of conversion of energy."

Effective Resistance. This is measured1 as "the quotient of the average rate of dissipation of electric energy during a cycle divided by the square of the effective current."

Resistance is given by the equation

where R is the resistance in ohms, P is the power in watts, and I is the current in amperes.

When direct current is flowing in a circuit energy is dissipated in forcing the electrons through the wires. When alternating current is flowing through, there are additional losses. In communication circuits and apparatus, such as inductors, or coils, and capacitors, or condensers, the most important alternating-current and voltage losses are as follows:

Direct-Current Resistance Loss. One component of the alternating-current loss is the loss that would occur with direct current.

Skin-Effect Loss. When an alternating current flows through a wire, the rapidly changing magnetic field causes the current in the wire to crowd to the surface. This phenomenon is called skin effect. This reduces the cross-sectional area of the wire that is effective in carrying current, and the effective resistance is therefore greater than the direct-current resistance because of the skin-effect loss.

Magnetic Hysteresis Loss. Energy is required to reverse a magnetic field in a ferromagnetic material such as the core of a transformer. Thus, if an alternating current produces an alternating magnetic field in ferromagnetic material, a magnetic hysteresis loss occurs. The loss is directly proportional to the frequency.

Eddy-Current Loss. An alternating magnetic field induces voltages in objects in the vicinity, and, if the objects are conducting, eddy currents flow. These eddy currents will dissipate energy in the resistances of their paths and will cause an eddy-current loss. For eddy-current flow in transformer-core laminations the loss varies as the squares of the frequency and the thickness of the laminations.

Dielectric Hysteresis Loss. When an alternating voltage is impressed on a capacitor, an alternating electric field is established in the dielectric. Energy is dissipated in reversing this field. This is called a dielectric hysteresis loss. Such losses also occur in insulators, in the insulation of coils, and in all objects through which an alternating electric field passes. If the power loss per cycle is assumed to be constant, then the loss is directly proportional to the frequency.