27_Ch 18 College Physics ProblemCH18 Direct-Current Circuits

27_Ch 18 College Physics ProblemCH18 Direct-Current...

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Direct-Current Circuits 125 (c) If the sodium ions enter the axon in a time of 2.0 ms t ∆ = , the average current is 9 7 3 1.67 10 C 8.3 10 A 0.83 2.0 10 s Q I t A µ ∆× == = (d) When the membrane becomes permeable to sodium ions, the initial influx of sodium ions neutralizes the capacitor with no required energy input. The energy input required to charge the now neutral capacitor to the potential difference of the excited state is () ( ) 2 2 83 11 1.67 10 F 30 10 V 7.5 10 J 22 f WCV −− =∆= × × 1 2 18.42 The capacitance of the 10 cm length of axon was found to be C in the solution of Problem 18.41. 8 1.67 10 F (a) When the membrane becomes permeable to potassium ions, these ions flow out of the axon with no energy input required until the capacitor is neutralized. To maintain this outflow of potassium ions and charge the now neutral capacitor to the resting action potential requires an energy input of ( ) 2 2 1.67 10 F 70 10 V 4.1 10 J × × 1 1 . (b) As found in the solution of Problem 18.41, the charge on the inner surface of the membrane in the resting state is and the charge on this surface in the
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