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57. (a) The power factor is cos
φ
, where
is the phase constant defined by the expression
i = I
sin(
ω
t
–
). Thus,
= – 42.0° and cos
= cos(– 42.0°) = 0.743.
(b) Since
< 0,
t
–
>
t
. The current leads the emf.
(c) The phase constant is related to the reactance difference by tan
= (
X
L
– X
C
)/
R
. We
have
tan
= tan(– 42.0°) = –0.900,
a negative number. Therefore,
X
L
– X
C
is negative, which leads to
X
C
> X
L
. The circuit in
the box is predominantly capacitive.
(d) If the circuit were in resonance
X
L
would be the same as
X
C
, tan
would be zero, and
would be zero. Since
is not zero, we conclude the circuit is not in resonance.
(e) Since tan
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This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
 Spring '08
 Any
 Physics, Current, Power

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