Let a series RLC network be connected to a source voltage V , drawing a current I . (a) In terms of the load impedance Z = Z ∠ Z , find expressions for P and Q, from complex power considerations. (b) Express p ( t ) in terms of P and Q, by choosing i ( t ) = 2 I cos ω t . (c) For the case of Z = R + j ω L + 1 / j ω C , interpret the result of part (b) in terms of P, Q L , and Q c . In particular, if ω 2 LC = 1 , when the inductive and capacitive reactances cancel, comment on what happens.
Let a series RLC network be connected to a source voltage V , drawing a current I . (a) In terms of the load impedance Z = Z ∠ Z , find expressions for P and Q, from complex power considerations. (b) Express p ( t ) in terms of P and Q, by choosing i ( t ) = 2 I cos ω t . (c) For the case of Z = R + j ω L + 1 / j ω C , interpret the result of part (b) in terms of P, Q L , and Q c . In particular, if ω 2 LC = 1 , when the inductive and capacitive reactances cancel, comment on what happens.
Solution Summary: The expression for P and Q is I2Zmathrmcos
Let a series RLC network be connected to a source voltage V, drawing a current I.
(a) In terms of the load impedance
Z
=
Z
∠
Z
, find expressions for P and Q, from complex power considerations.
(b) Express
p
(
t
)
in terms of P and Q, by choosing
i
(
t
)
=
2
I
cos
ω
t
. (c) For the case of
Z
=
R
+
j
ω
L
+
1
/
j
ω
C
, interpret the result of part (b) in terms of
P,
Q
L
, and
Q
c
. In particular, if
ω
2
LC
=
1
, when the inductive and capacitive reactances cancel, comment on what happens.
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Reactance of a circuit is always expressed as real number and comprised the imaginary part of the impedance equation.
O True
O False
"In phasor, the reactance has an angle of 0 degrees and the voltage and current are in phase."
O True
O False
Chapter 2 Solutions
Power System Analysis and Design (MindTap Course List)
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