# TAILIEUCHUNG - Alternating Currents

## The general topic of alternating current (AC) inﬂuence on the battery charging is necessarily a huge undertaking. The vast body of knowledge in electrochemical systems has been largely associated with direct current (DC) measurements. To place this into perspective, it helps to note that a DC can be considered a special case of an AC where the frequency of the AC is zero (or, as a practical matter, has a frequency having a very long period). | Alternating Currents HA Catherine US Army Research Development and Engineering Command AMSRD-TAR-R MS 121 Warren MI USA 2009 Elsevier . All rights reserved. Introduction The general topic of alternating current AC influence on the battery charging is necessarily a huge undertaking. The vast body of knowledge in electrochemical systems has been largely associated with direct current DC measurements. To place this into perspective it helps to note that a DC can be considered a special case of an AC where the frequency of the AC is zero or as a practical matter has a frequency having a very long period . In order to keep this presentation within reasonable limits it will be presented as a collection of special interest topics that are connected with AC issues. Hopefully this will give an indication of the breadth and the scope of the AC influence. Root Mean Square Heating An AC applied to an electrochemical cell contributes no net charge to that cell. From a faradaic viewpoint the second half of the cycle undoes what was accomplished during the first half of the cycle. Alternatively from a resistive perspective the Joule heating is independent of the direction of the passing current. In the case of an applied AC it is helpful to estimate the effective value of that current that corresponds to an equivalent DC producing the same heating effect. In short the average power delivered to a resistor by a periodic current i t is 1 fT P Wo i2R dT where the period of i t is T The DC power delivery is P i2ff R so the effective current affecting the Joule heating is In the case of a sinusoidal waveform I Im eff V2 where Im is the maximum instantaneous current that characterizes the waveform. That is Im is the absolute value of the peak current delivered by the applied sinusoidal current. This RMS heating may or may not be a concern in any particular application. Since it does introduce a heating effect into an electrochemical cell this necessitates an increase in temperature

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