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In-Class Exercises

Pb. 6.31 This problem pertains to the RC circuit:
a. Write the output signal V in the amplitude-phase representation.
C
b. Plot the gain response as a function of a normalized frequency that
you will have to select. (The gain of a circuit is defined as the ratio
of the amplitude of the output signal over the amplitude of the
input signal.)
c. Determine the phase response of the system (i.e., the relative phase
of the output signal to that of the input signal as function of the
frequency) also as function of the normalized frequency.
d. Can this circuit be used as a filter (i.e., a device that lets through only
a specified frequency band)? Specify the parameters of this band.
Pb. 6.32 This problem pertains to the RLC circuit:
a. Write the output signal V in the amplitude-phase representation.
C
b. Defining the resonance frequency of this circuit as: ω = 1 , find
0
LC
at which frequency the gain is maximum, and find the width of
the gain curve.
c. Plot the gain curve and the phase curve for the following cases:
ω L
0
= 0.1, 1, 10 .
R
d. Can you think of a possible application for this circuit?
Pb. 6.33 Can you think of a mechanical analog to the RLC circuit? Identify
in that case the physical parameters in the corresponding ODE.
Pb. 6.34 Assume that the source potential in the RLC circuit has five fre-
quency components at ω, 2ω, …, 5ω of equal amplitude. Plot the input and
output potentials as a function of time over the interval 0 < ωt < 2π. Assume
that ω = ω = 1 and ω L = 1.
0
0
LC R

6.6 Phasors
A technique in widespread use to compute the steady-state solutions of sys-
tems with sinusoidal input is the method of phasors. In this and the following
two chapter sections, we define phasors, learn how to use them to add two or

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