A single-phase, 120 − V ( rms ) , 60 − Hz source supplies power to a series R-L circuit consisting of R = 10 Ω and L = 40 mH . (a) Determine the power factor of the circuit and state whether it is lagging or leading. (b) Determine the real and reactive power absorbed by the load. (c) Calculate the peak magnetic energy W int stored in the inductor by using the expression W int = L ( I rms ) 2 and check whether the reactive power Q = ω W int is satisfied. ( Note: The instantaneous magnetic energy storage fluctuates between zero and the peak energy. This energy must be sent twice each cycle to the load from the source by means of reactive power flows.)
A single-phase, 120 − V ( rms ) , 60 − Hz source supplies power to a series R-L circuit consisting of R = 10 Ω and L = 40 mH . (a) Determine the power factor of the circuit and state whether it is lagging or leading. (b) Determine the real and reactive power absorbed by the load. (c) Calculate the peak magnetic energy W int stored in the inductor by using the expression W int = L ( I rms ) 2 and check whether the reactive power Q = ω W int is satisfied. ( Note: The instantaneous magnetic energy storage fluctuates between zero and the peak energy. This energy must be sent twice each cycle to the load from the source by means of reactive power flows.)
Solution Summary: The author states the power factor of the circuit and state whether it is lagging or leading.
A single-phase,
120
−
V
(
rms
)
,
60
−
Hz
source supplies power to a series
R-L
circuit consisting of
R
=
10
Ω
and
L
=
40
mH
. (a) Determine the power factor of the circuit and state whether it is lagging or leading. (b) Determine the real and reactive power absorbed by the load. (c) Calculate the peak magnetic energy
W
int
stored in the inductor by using the expression
W
int
=
L
(
I
rms
)
2
and check whether the reactive power
Q
=
ω
W
int
is satisfied. (Note: The instantaneous magnetic energy storage fluctuates between zero and the peak energy. This energy must be sent twice each cycle to the load from the source by means of reactive power flows.)
10.29 A 208-V (rms) balanced three-phase source supports twoloads connected in parallel. Each load is itself a balanced threephaseload. Determine the line current, given that load 1 is 12 kVAat pf 1 = 0.7 leading and load 2 is 18 kVA at pf 2 = 0.9 lagging.
10.31 A 240-V (rms), 60-Hz Y-source is connected to a balancedthree-phase Y-load by four wires, one of which is the neutral wire.If the load is 400 kVA at pf old = 0.6 lagging, what size capacitorsshould be added to change the power factor to pf new = 0.95lagging?
Cable A
Cable A is a coaxial cable of constant cross section. The metal
regions are shaded in grey and are made of copper. The solid central
wire has radius a = 5mm, the outer tube inner radius b = 20mm and
thickness t = 5mm. The dielectric spacer is Teflon, of relative
permittivity &r = 2.1 and breakdown strength 350kV/cm. A potential
difference of 1kV is applied across the conductors, with centre
conductor positive and outer conductor earthed.
Before undertaking any COMSOL simulations we'll first perform some theoretical analysis
of Cable A based on the EN2076 lectures, to make sense of the simulations. Calculate the
radial electric field of cable A at radial positions r b. Also calculate the
maximum operating voltage of cable A, assuming a safety margin of ×2, and indicate where
on the cable's cross section dielectric breakdown is most likely to occur.
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