# 1 Each phase of a ∆-connected load consists of the series

```Each phase of a -connected load consists of the series combination of a 350-mH inductor,
a 20-F capacitor, and a 170- resistance. This load is fed by a Y-connected source.
The source has a positive phase sequence and Va  4000 VRMS .
Assume zero line resistance and  = 1000 rad/s.
Determine the total average power absorbed by the load.
Spring 2014, Exam #2, Problem #1
1
In the circuit shown, the three-phase source is balanced with a positive phase sequence
and va  169.7cos  377t  V .
Each of the inductors is 46 mH and each of the resistors is 10 .
Determine the total average power absorbed by the Y load.
Spring 2015, Exam #3, Problem #1
2
For the circuit given, determine the magnitude of the neutral-to-neutral voltage, |VNn| .
Spring 2015, Exam #3, Problem #2
3
In the circuit shown, the three-phase source is balanced with a positive phase sequence
and Va  86.70 VRMS . Let Z1  Z2  Z3  15  26 j  .
Determine the average power absorbed by phase impedance Z2 .
Spring 2015, Exam #3, Problem #3
4
In the circuit shown, the source is balanced with a positive phase sequence
and va  240cos  377t  V .
Load A is a 40- resistor and a 184-mH inductor in series.
Load B is a 51-F capacitor and a 30- resistor in series. Load C is a 16- resistor.
Determine the neutral-to-neutral current, iNn(t) .
Spring 2015, Exam #3, Problem #4
Answer: 8cos  377t  120 A
5
A Y-source is balanced with a negative phase sequence and Va  2000 VRMS .
This source is connected to a Y-load where each phase impedance is 28  37 j  .
The line impedance between each source phase and each load phase is 2  3 j  .
Determine the total average power absorbed by the lines.
Spring 2015, Exam #3, Problem #5
6
A balanced -connected load with Z P  8  6 j  is connected to
a balanced Y-connected source with Van  163.30 V and a positive phase sequence.
Assume that the line impedances between the source and the load are negligible.
Calculate the total average power absorbed by the load.
Spring 2015, Final exam, Problem #5
7
In the circuit below, the Y source has a positive phase sequence with Va  1100 VRMS .
The load impedances are ZA  50  j80  , ZB  j50  , ZC  100  j 25  .
Determine the complex power delivered to ZA .
Spring 2015, Final exam, Problem #6
8
In the circuit below, the resistor markings unfortunately have been omitted, but several of the
currents are known. Specifically, Iad = 1 A. (a) Compute Iab , Icd , Ide , Ife , and Ibe .
(b) If Vba = 125 V , determine the value of the resistor linking nodes a and b .
Spring 2014, Homework #4, Problem #3
Answers: (a) Iab = –9 A , Icd = 8 A , Ide = 9 A , Ife = –10 A , Ibe = 1 A , (b) 13.9 
9
Assume the system shown below is balanced, Rw = 0 , Van = 208 V , and a positive phase
sequence applies. Calculate all phase and line currents, and all phase and line voltages, if Zp is
equal to (a) 1 k , (b) 100 + j48  , (c) 100 – j48  .
Spring 2014, Homework #4, Problem #5
Van  2080 V
Van  2080 V
Van  2080 V
Vbn  208  120 V
Vbn  208  120 V
Vbn  208  120 V
Vcn  208  240 V
Vcn  208  240 V
Vcn  208  240 V
Answers: (a) Vab  36030 V
, (b) Vab  36030 V
, (c) Vab  36030 V
Vbc  360  90 V
Vbc  360  90 V
Vbc  360  90 V
Vca  360  210 V
Vca  360  210 V
Vca  360  210 V
I aA  2080 mA
I aA  1.87  25.8 A
I aA  1.8725.8 A
I bB  208  120 mA
I bB  1.87  145.8 A
I bB  1.87  94.2 A
I cC  208  240 mA
I cC  1.87  265.8 A
I cC  1.87145.8 A
10
For the balanced three-phase system shown below, it is determined that 100 W is lost in each
wire. If the phase voltage of the source is 400 V , and the load draws 12 kW at a lagging power
factor of 0.83, determine the wire resistance Rw .
Spring 2014, Homework #4, Problem #6
11
The balanced circuit shown below has Vab = 380 VRMS .
Determine the line and phase currents in the load when Z = 9 + j12  .
Spring 2015, Homework #4, Problem #2
I aA  14.67  83.1 A RMS
Answers: I bB  14.67  203.1 A RMS
I cC  14.67  36.9 A RMS
12
A three-phase balanced load is fed by a balanced Y-connected source with a line-to-line voltage
of 220 VRMS . It absorbs 1500 W at 0.8 power factor lagging. Calculate the phase impedance if
it is (a)  connected , and (b) Y connected .
Spring 2015, Homework #4, Problem #3
Answers: (a) 61.9 + j46.5  , (b) 20.6 + j15.5 
13
Determine the power delivered to the load in the circuit below.
Spring 2015, Homework #4, Problem #4
14
In the circuit below, each impedance Zp is a parallel combination of a 1-mF capacitance, a 100mH inductance, and a 10- resistance. One line voltage is Vab  2080 V . The sources have a
positive phase sequence and operate at 50 Hz. Each wire resistance is Rw = 1 . Determine the
total (real) power absorbed by the load.
Spring 2016, Homework #4, Problem #3
15
In Circuit #4, determine the line current IcC .
Spring 2016, Homework #4, Problem #4
16
In the circuit below, the balanced Delta-connected load draws a total
apparent power of 15 kVA at a lagging power factor of 0.87 .
The source is balanced and follows a positive phase sequence.
One phase voltage is Van  1700 V . The line impedances are negligible.
Determine the RMS amplitude of the line current IbB .
Spring 2016, Exam #2, Problem #3
17
A balanced three-phase, negative-sequence, Wye-connected source with
Vcn  2400 VRMS is connected to a three-phase Wye-connected load.
Each phase of the load has an impedance of 10 + j15 Ω .
The impedances in the lines are ZaA = 1 + j3 Ω , ZbB = 2 + j2 Ω , ZcC = 1 + j2 Ω .
Determine the RMS amplitude of the line current into phase C of the load.
Spring 2016, Exam #2, Problem #4