Physics 21
Fall, 2008
Solution to HW19
316
A capacitance
C
and an inductance
L
are operated at
the same angular frequency. (a) At what angular frequency
will they have the same reactance?
(b) If
L
=4
.
80 mH
and
C
=3
.
70
µ
F, what is the numerical value of the angular
frequency in part (a)?
(c) What is the reactance of each
element?
(a) Equate the reactances and solve for
ω
:
1
ωC
=
ωL
⇒
1=
ω
2
LC
⇒
ω
=
1
√
LC
.
(b) Substituting numbers,
ω
=
1
p
(4
.
80
×
10

3
)(3
.
70
×
10

6
)
=7
.
50
×
10
3
rad
/
s
.
(c) Again substituting numbers,
1
ωC
=
ωL
=36
.
0Ω
.
319
(a) What is the reactance of an inductor with an
inductance of 3.40 H at a frequency of 84.0 Hz? (b) What
is the inductance of an inductor whose reactance is 11.3 Ω
at a frequency of 84.0 Hz? (c) What is the reactance of a
capacitor with a capacitance of 3
.
56
×
10

6
F at a frequency
of 84.0 Hz? (d) What is the capacitance of a capacitor whose
reactance is 113 Ω at a frequency of 84.0 Hz?
(a)
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This note was uploaded on 02/09/2009 for the course PHYS 021 taught by Professor Hickman during the Fall '08 term at Lehigh University .
 Fall '08
 Hickman
 Capacitance, Inductance

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