answer questions (show work, include each step for how to get to the final answer)

1. Axons in the brain have smaller diameters than motor neurons; 0.6 μm is a typical value. Most connections are short range, with an average axon length of about 700 μm. The resistivity of the 7-nm-thick axon membrane is approximately 4×107 Ω; the dielectric constant is 5. Model the axon as a cylinder. (6 pts)
Find out and show your work
(a) the resistance in MΩ,
(b) the capacitance in μF, and
(c) the time constant in ms of the axon membrane?
2. The giant axon of a squid is 0.5 mm in diameter, 10 cm long, and not myelinated. Unmyelinated cell membranes behave as capacitors with 1 μF of capacitance per square centimeter of membrane area. When the axon is charged to the −70 mV resting potential, what is the energy stored in this capacitance? (4 pts) Show your work
3. A myelinated nerve fiber has a 4.0-μm-diameter cylindrical axon covered by a 1.0-μm-thick layer of myelin. No ions pass through the axon membrane, which is sealed by the myelin, but an action potential at a node causes an ion current to flow along the axis of the axon. The axon is filled with cytosol, whose resistivity was given in Chapter 24 as 0.50 Ω⋅m The dielectric constant of myelin is assumed to be 5.0, the same as that of the cell membrane (8 pts) Show your work.
a) What are the capacitance in pF and the resistance in MΩ of a 1.0-mm-long segment of a myelinated nerve fiber? Use the average radius of the myelin sheath for calculating capacitance.
b) What is the time constant in μs of this RC circuit