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C = πε 0 (3.16)
l −1  D 
cosh
 2 a 

where ε is the permittivity of air (taken to be that of vacuum) = 8.854 × 10 –12
0
Farad/m.
Question: Write this expression in a different form using the logarithmic
function.

In-Class Exercises
Pb. 3.28 Find the capacitance per unit length of two wires of radii 1 cm sep-
arated by a distance of 1 m. Express your answer using the most appropriate
of the following sub-units:

mF = 10 −3 F (milli-Farad); µ F = 10 –6 F (micro-Farad);
nF = 10 −9 F (nano-Farad); pF = 10 −12 F (pico-Farad);
fF = 10 −15 F (femto-Farad); aF = 10 −18 F (atto-Farad);

Pb. 3.29 Assume that you have two capacitors, one consisting of a coaxial
cable (radii a and b) and the other of two parallel wires, separated by the dis-
tance D. Further assume that the radius of the wires is equal to the radius of
D b
the inner cylinder of the coaxial cable. Plot the ratio as a function of ,
a a
if we desire the two geometrical configurations for the capacitor to end up
 ε 
having the same value for the capacitance. Take = 26.. 

 ε 0 

3.9 Commonly Used Signal Processing Functions

In studying signals and systems, you will also encounter, inter alia, the fol-
lowing functions (or variation thereof), in addition to the functions discussed
previously in this chapter:

• Unit step function
• Unit slope ramp function

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