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(i) RC = 1
(ii) RC = 5
(iii) RC = 10
Which of these time constants results in the fastest approach of V (t) toward V ?
c
s
c. Repeat the above simulations for the case V = 0 (capacitor dis-
s
charge)?
d. What would you expect to occur if V (0) = V ?
c
s

Homework Problem

Pb. 3.27 The Fermi-Dirac distribution, which gives the average population
of electrons in a state with energy ε, neglecting the electron spin for the
moment, is given by:

1
f()ε =
exp[(εµ− )/ ] + 1Θ

where µ is the Fermi (or chemical) potential and Θ is proportional to the abso-
lute (or Kelvin) temperature.
a. Plot the function f(ε) as function of ε, for the following cases:
(i) µ = 1 and Θ = 0.002
(ii) µ = 0.03 and Θ = 0.025
(iii) µ = 0.01 and Θ = 0.025
(iv) µ = 0.001 and Θ = 0.001
b. What is the value of f(ε) when ε = µ?
c. Determine the condition under which we can approximate the
Fermi-Dirac distribution function by:

f(ε) ≈ exp[(µ – ε)/Θ]

3.8 Examples with the Hyperbolic Functions and Their
Inverses

3.8.1 Capacitance of Two Parallel Wires
The capacitance per unit length of two parallel wires, each of radius a and
having their axis separated by distance D, is given by:

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