Passage Cable Theory Is a Mathematical Model Used to Calculate Currents

Passage
Cable theory is a mathematical model used to calculate currents and voltages along and across axon membranes.  The model treats small sections of the membrane as the resistor-capacitor circuit shown in Figure 1.  An electric neuronal signal enters the circuit through the input node.  A portion of the signal remains inside the axon and continues to the next section of membrane via Output 1, and the rest of the signal exits to the extracellular fluid via Output 2.
Figure 1  Circuit unit used to model axon membranesResearchers studied cable theory by recreating the circuit in Figure 1 using a 2 μF capacitor for C_M, a 200 Ω resistor for R_M, and a 1,000 Ω resistor for R_L.  The researchers sent an electrical signal through the input and discovered that the capacitor acted as a resistor whose resistance varied with the signal's frequency, as shown in Figure 2.
Figure 2  Capacitor equivalent resistance vs. signal frequency for C_M
Adapted from Tuckwell H, Introduction to Theoretical Neurobiology 2006 SIAM.
-To test the integrity of the capacitor, researchers maintained a voltage of 50 mV across the parallel portion of the circuit for several minutes.  During this time, how much energy was stored in the capacitor?

A) 2.5 × 10⁻⁹ J
B) 5.0 × 10⁻⁹ J
C) 5.0 × 10⁻⁸ J
D) 1.0 × 10⁻⁷ J

Correct Answer:

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