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.
The output voltage of an AC generator is given by Δ v = (170 V) sin (60πt). The generator is connected across a 20.0-Ω resistor. By inspection, what are the (a) maximum voltage and (b) frequency? Find the (c) rms voltage across the resistor, (d) rms current in the resistor, (e) maximum current in the resistor, (f) power delivered to the resistor, and (g) current when t = 0.005 0 s. (h) Should the argument of the sine function be in degrees or radians?
Step 1
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GIVEN:
Output voltage, Δv = (170 V) sin (60πt)
Resistance, R = 20.0-Ω
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Step 2 Part (a)
Part (a)
Standard equation can be represented as,
Δv = Vmsin(ωt)
Where, Vm = maximum voltage.
ω = angular frequency.
Compare the given equation with standard equation.
We get, Vm…
The output voltage of an AC generator is given by Δ v = (170 V) sin (60πt). The generator is connected across a 20.0-Ω resistor. By inspection, what are the (a) maximum voltage and (b) frequency? Find the (c) rms voltage across the resistor, (d) rms current in the resistor, (e) maximum current in the resistor, (f) power delivered to the resistor, and (g) current when t = 0.005 0 s. (h) Should the argument of the sine function be in degrees or radians?
GIVEN:
Output voltage, Δv = (170 V) sin (60πt)
Resistance, R = 20.0-Ω
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Step 2 Part (a)
Part (a)
Standard equation can be represented as,
Δv = Vmsin(ωt)
Where, Vm = maximum voltage.
ω = angular frequency.
Compare the given equation with standard equation.
We get, Vm = 170 V Answer
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Step 3 Part (b)
Part (b)
Angular frequency, ω = 60π ... (1)
Also, ω = 2πf .... (2)
Equate both,
2πf = 60π
f = 60π/2π
f = 30 Hz Answer
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Step 4 Part (c)
Part (c)
RMS voltage is…
The emf of an ac source is given by v(t) = V0 sin ωt, where V0 = 100 V andω = 200π rad/s. Calculate the average power output of the source if it is connected across (a) a 20-μF capacitor, (b) a 20-mH inductor, and (c) a 50-Ω resistor.
Chapter 30 Solutions
Physics for Science and Engineering With Modern Physics, VI - Student Study Guide
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