p33_077.pdf

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77. (a) With
f
understood to be in Hertz, the capacitive reactance is
X
C
= (2π)(45
×
10
−6
F)f
−1
.
(b) The resistance, reactance and impedance are plotted over the range 10
≤
f
≤
70 Hz. The horizontal
line is
R,
and the curve that crosses that line is
X
C
. SI units are understood.
400
350
300
250
200
150
100
50
10
20
30
40
f
50
60
70
(c) From the graph, we estimate the crossing point to be at about 18 Hz. More careful considerations
lead to
f
= 17.7 Hz as the frequency where
X
C
=
R.

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