218 THREE-PHASE CIRCUITS AND RESIDENTIAL WIRINGProblems
*4.1.1The line-to-line voltage of a balanced wye-
connected three-phase source is given as 100 V.
ChooseVABas the reference.
(a) For the phase sequenceA–B–C, sketch the
phasor diagram of the voltages and find the
expressions for the phase voltages.
(b) Repeat part (a) for the phase sequenceC–B–A.
4.2.1A three-phase, three-wire 208-V system is con-
nected to a balanced three-phase load. The line
currentsI ̄A,I ̄B, andI ̄Care given to be in phase
with the line-to-line voltagesV ̄BC,V ̄CA, andV ̄AB,
respectively. If the line current is measured to be
10 A, find the per-phase impedance of the load.
(a) If the load is wye-connected.
(b) If the load is delta-connected.
*4.2.2Consider a three-phase 25-kVA, 440-V, 60-Hz
alternator operating at full load (i.e., delivering
its rated kVA) under balanced steady-state condi-
tions. Find the magnitudes of the alternator line
current and phase current.
(a) If the generator windings are wye-connected.
(b) If the generator windings are delta-connected.
4.2.3Let the alternator of Problem 4.2.2 supply a line
current of 20 A at a power factor of 0.8 lagging.
Determine:
(a) The kVA supplied by the machine.
(b) The real power kW delivered by the generator.
(c) The reactive power kVAR delivered by the
alternator.
4.2.4A balanced wye-connected load with a per-phase
impedance of 4+j 3 is supplied by a 173-V,
60-Hz three-phase source.
(a) Find the line current, the power factor, the total
volt-amperes, the real power, and the reactive
power absorbed by the load.
(b) Sketch the phasor diagram showing all the
voltages and currents, withV ̄ABas the ref-
erence.
(c) If the star point of the load is connected to
the system neutral through an ammeter, what
would the meter read?
4.2.5A balanced delta-connected load with a per-phase
impedance of 12+j 9 is supplied by a 173-V,
60-Hz three-phase source.
(a) Determine the line current, the power factor,
the total volt-amperes, the real power, and the
reactive power absorbed by the load.
(b) Compare the results of Problem 4.2.5(a) with
those obtained in Problem 4.2.4(a), and ex-
plain why they are the same.
(c) Sketch the phasor diagram showing all volt-
ages and currents, withV ̄ABas the reference.
4.2.6A 60-Hz, 440-V, three-phase system feeds two
balanced wye-connected loads in parallel. One
load has a per-phase impedance of 8+j 3 and
the other 4−j 1 . Compute the real power in
kW delivered to (a) the inductive load, and (b) the
capacitive load.
*4.2.7Balanced wye-connected loads drawing 10 kW
at 0.8 power factor lagging and 15 kW at 0.9
power factor leading are connected in parallel and
supplied by a 60-Hz, 300-V, three-phase system.
Find the line current delivered by the source.
4.2.8A balanced delta-connected load with a per-phase
impedance of 30+j 10 is connected in parallel
with a balanced wye-connected load with a per-
phase impedance of 40−j 10 . This load combi-
nation is connected to a balanced three-phase sup-
ply through three conductors, each of which has a
resistance of 0.4. The line-to-line voltage at the
terminals of the load combination is measured to
be 2000 V. Determine the power in kW:
(a) Delivered to the delta-connected load.
(b) Delivered to the wye-connected load.
(c) Lost in the line conductors.
4.2.9Three identical impedances of 3030°are con-
nected in delta to a three-phase 173-V system by
conductors that have impedances of 0. 8 +j 0. 6
each. Compute the magnitude of the line-to-line
voltage at the terminals of the load.
4.2.10Repeat Problem 4.2.9 for a delta-connected set of
capacitors with a per-phase reactance of−j 60
connected in parallel with the load, and compare
the result with that obtained in Problem 4.2.9.
4.2.11Two balanced, three-phase, wye-connected loads
are in parallel across a balanced three-phase sup-
ply. Load 1 draws a current of 20 A at 0.8 power
factor leading, and load 2 draws a current of 30
A at 0.8 power factor lagging. For the combined
load compute: