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Problem Set # 6 (1 block total) Complete the following problem presented to you on Monday, March 28th (Le Problem Set 6: Step Current Setup Part 1. Consider cylindrical nerve fiber of radius 40 um covered by a thin film of thickness 30um. The conductivity of the nerve fiber and fluid film are given at 1.0 S/m and 2.0 S/m respectively. 1. Solve for R, and R., and further determine r., r.. 2. Determine the length constant when R= 10.0 kn. m Part 2. We shall next probe this fiber with a step current, where we inject l, = 50 uA. Let the probe be denoted at position x = 0. 3. Draw out the appropriate experimental setup to solve Q4. 4. What would v (1.5 mm) be at steady-state? Be sure to additionally include the general form of the steady-state solution.
solution. Problem Set 6: Dimensionless Analysis Part 3: Continue with the cylindrical nerve fiber and the experiment setup from the previous page. Now onto the Dimensionless Analysis: 1. Let time constant t = 1. Determine the fraction of steady-state reached by v for λ = [0, 6]. This is a plot mapping the ratio of time-dependent vm(2, t) vs vm at steady-state. 2. From this plot, what are these ratios at 0.52, 1.5, and 2.5? Further comment on the plot when exceeding 32. 3. Finally, what would the behavior be for different t?