An ac voltage source V = V 0 sin ( ω t + 90 ° ) is connected across an inductor L and current I = I 0 sin ( ω t ) flows in this circuit. Note that the current and source voltage are 90º out of phase. ( a ) Directly calculate the average power delivered by the source over one period T of its sinusoidal cycle via the integral P ¯ = ∫ 0 T V I d t / T . ( b ) Apply the relation P ¯ = I r m s V r m s cos ϕ this circuit and show that the answer you obtain is consistent with that found in part ( a ) . Comment on your results.
An ac voltage source V = V 0 sin ( ω t + 90 ° ) is connected across an inductor L and current I = I 0 sin ( ω t ) flows in this circuit. Note that the current and source voltage are 90º out of phase. ( a ) Directly calculate the average power delivered by the source over one period T of its sinusoidal cycle via the integral P ¯ = ∫ 0 T V I d t / T . ( b ) Apply the relation P ¯ = I r m s V r m s cos ϕ this circuit and show that the answer you obtain is consistent with that found in part ( a ) . Comment on your results.
An ac voltage source
V
=
V
0
sin
(
ω
t
+
90
°
)
is connected across an inductor L and current
I
=
I
0
sin
(
ω
t
)
flows in this circuit. Note that the current and source voltage are 90º out of phase. (a) Directly calculate the average power delivered by the source over one period T of its sinusoidal cycle via the integral
P
¯
=
∫
0
T
V
I
d
t
/
T
. (b) Apply the relation
P
¯
=
I
r
m
s
V
r
m
s
cos
ϕ
this circuit and show that the answer you obtain is consistent with that found in part (a). Comment on your results.
An inductor (L = 420 mH), a capacitor (C = 4.43 µF), and a resistor (R = 510 Ω) are connected in series. A 50.0-Hz AC source produces a peak current of 250 mA in the circuit.
(a) Calculate the required peak voltage ΔVmax. ????? V(b) Determine the phase angle by which the current leads or lags the applied voltage.
magnitude ????? (in degrees)
direction
---Select---
leads
lags
The voltage of an ac source is given by V(t) = Vo sin wt, where Vo = 100 V and w= 180 rad/s.
Calculate the average power output of the source if it is connected across (a) a 35-µF capacitor, (b) a 45-
mH inductor, and (c) a 60-02 resistor. (d) What is the rms voltage of the ac source?
Hint
a. The average power output with the capacitor is
b. The average power output with the inductor is
c. The average power output with the resistor is
d. The rms voltage of the ac source is
Quartion Moint 52 Morrago instructor
W.
W.
W.
V. Additional Hints
An inductor (L = 420 mH), a capacitor (C = 4.43 µF), and a resistor (R = 440 2) are connected in series. A 50.0-Hz AC source
produces a peak current of 250 mA in the circuit.
(a) Calculate the required peak voltage AV,
max
123.1
Your response differs from the correct answer by more than 10%. Double check your calculations. V
(b) Determine the phase angle by which the current leads or lags the applied voltage.
magnitude 53.1
direction
leads
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Chapter 30 Solutions
Physics for Scientists and Engineers with Modern Physics
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