Effective Resistance

Author: E.E. Kimberly

By equation (2-2), which is based on Joule's Law,

(5-20)

If the resistance of a solenoid containing an iron core be computed by equation (5-20), and if the voltage be alternating and P be measured by a wattmeter, the power indicated by the wattmeter will include that converted into heat in the copper of the coil and also that caused by eddy currents and hysteresis loss in the iron of the core.

The reason for these iron losses is discussed in Chapter 7. The resistance so calculated would be greater, of course, than that which would have been found if direct current had been used, because direct current can produce power loss only in the copper of the coil. The value of the resistance found by a direct-current test is called the ohmic resistance. The resistance found by using alternating current is called effective resistance and is denoted by Re. The difference between measured ohmic resistance and effective resistance is determined largely by the quality and structure of the iron core. Effective resistance is also somewhat different from ohmic resistance because the alternating current does not distribute itself over the cross-section of its conductor so effectively as does direct current, and the alternating current sets up localized eddy currents in the conductor which contribute further to the power loss and hence to the increase in the effective resistance.

Fig. 5-27. Transposition of Grouped Conductors to Mitigate Eddy-Current Losses

For this reason, when a large conductor must be used, it is usually made up of several smaller conductors grouped together and periodically transposed among themselves in the group so that in the total length of the conductor every one of the small component conductors has occupied every position in the group at least once, as shown in Fig. 5-27.