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Unformatted text preview: 10.626 Electrochemical Energy Systems Spring 2011 MIT, M. Z. Bazant Problem Set 2 Equivalent Circuits, Thermodynamics Due: Lecture 11 1. Equivalent circuit for a supercapacitor. (a) Derive the Warburg impedance of the form, Z W = A ( r,c ) / i , for an infinite RC transmission line (Fig. 1a) with resistance per length r and capacitance per length c . (b) The high frequency response of a supercapacitor, consisting of two porous electrodes and a thin separator region, can be described by two Warburg elements Z W and a resistance R s in series (Fig 1b). Make a Nyquist plot of Im Z vs. Re Z , and Bode plots of ln | Z | and arg( Z ) vs. ln for this equivalent circuit. (c) As shown in problem set 1, the long time (low frequency) response of a porous electrode of length L is that of the total resistance R = rL in series with the total capacitance C = cL . Devise an equivalent circuit that smoothly connects this low frequency regime (Fig 1c) for RC 1 to the high frequency regime...
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- Spring '03