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# MCQ in AC Circuits Part 8 | REE Board Exam

This is the Multiple Choice Questions Part 8 of the Series in AC Circuits as one of the Electrical Engineering topic. In Preparation for the REE Board Exam make sure to expose yourself and familiarize in each and every questions compiled here taken from various sources including but not limited to past Board Exam Questions in Electrical Engineering field, Electrical Engineering Books, Journals and other Electrical Engineering References.

#### Continue Practice Exam Test Questions Part 8 of the Series

PARALLEL CIRCUITS

Choose the letter of the best answer in each questions.

351.ย  EE Board Exam April 1990

A capacitor, an electric resistance heater, andย impedance are connected in parallel to a 120ย V,ย 60 Hz system. The capacitor draws 50ย  var,ย  theย heater draws 100 W and the impedance coil draws 269 VA at a pf 0f 0.74 lagging. Determine the system power factor.

B.ย  0.928 lagging

C.ย  0.916 lagging

D.ย  0.911 lagging

Solution:

352.ย  REE Board Exam October 1996

Aย bankย of capacitors is connected in parallel each ratedย at 10 kVAR,ย 380 volts.ย If one unit is shortedย out,ย whatย  would be the net capacitanceย of the bank?

A.ย  330 ฮผF

B.ย  440 ฮผF

C.ย  220 ฮผF

D.ย  110 ฮผF

Solution:

353.ย  EE Board Exam October 1992

A capacitor of 3.18 microfarads is connected in parallel with a resistance of 2,000 ohms.ย Theย combinationย isย further connectedย  inย  seriesย  withย  an inductance of 795 mH and resistance of 100 ohms across a supply given by e = 400 sin ฯt + 80 sin (3ฯt + 60ยฐ). Assume w = 314 radians/sec. Determine the rms value of the total current.

A.ย  0.40 A

B.ย  0.33 A

C.ย  0.56 A

D.ย  0.45 A

Solution:

354.ย  EE Board Exam June 1990

Three loads, units A, B and C are connected in parallel and take currents that are respectively 12, 10ย and 15 Aย  respectively. Assumingย  Ia to beย the reference phasor. Ib leads Ia by 30ยฐ and Ic lags behind Ia by 65ยฐ, calculate the total (resultant) current.

A.ย  28.33 A

B.ย  30.21 A

C.ย  26.46 A

D.ย  32.10 A

Solution:

355.ย  EE Board Exam April 1992

Twoย  single-phaseย  motorsย  areย  connectedย  inย  parallelย  acrossย  aย  120-volt,ย  60-cycle source of supply. Motor A is a split-phase inductance type and motor B is a capacitor type:

Determine total power factor.

A.ย  0.886 lag

B.ย  0.864 lag

C.ย  0.817 lag

D.ย  0.825 lag

Solution:

356.ย  EE Board Exam April 1992

A 250 V, 30 Hz generator supplies power to a parallel circuit consisting of a 20 HP motor whose efficiency is 90% at 0.80 pf lagging and a second load that draws an apparent power of 7 kVA at unity pf.ย Determineย the system power factor.

A.ย  0.828 lagging

B.ย  0.831 lagging

C.ย  0.802 lagging

D.ย  0.884 lagging

Solution:

357.ย  EE Board Exam April 1985

A resistance of 5 ohms is connected in series with a capacitor of 442.1 ฮผF. The combination is then connected in parallel with an inductance ofย  21.22 mH. Solve for the resultant current if the circuit is connected across a 120 V, 60 Hz AC source.

A.ย  9.44 A

B.ย  10.68 A

C.ย  11.29 A

D.ย  10.34 A

Solution:

358.ย  EE Board Exam April 1993

An inductor L1 is connected in series with a parallel combination of inductor L2ย  and capacitorย  C.ย The impedance of the circuit wย  =ย  400 rad/sec is j100 ohms. The circuit is to yield infinite impedance at w = 1,000 rad/sec and zero impedance at w = 2,000 rad/sec. Determine the value of C.

A.ย  1.28 ฮผF

B.ย  1.67 ฮผF

C.ย  2.06 ฮผF

D.ย  1.32 ฮผF

Solution:

359.ย  EE Board Exam April 1992

A sinusoidalย  current source, 10 cos 1000t, is in parallel both with a 20-ohm resistorย  andย  theย  seriesย  combinationย  ofย  aย  10-ohmย  resistorย  andย  aย  10-mH inductor. Find the equation of the voltage across the 10 -ohm resistor.

A.ย  63.25 cos (1000t โ 18.43ยฐ)

B.ย  61.32 cos (1000t โ 20.34ยฐ)

C.ย  59.36 cos (1000t โ 17.45ยฐ)

D.ย  60.12 cos (1000t โ 19.38ยฐ)

360.ย  EE Board Exam April 1993

A 1-hp, 220 V, 60 Hz capacitor-start motor has main and auxiliary winding impedance at starting of 3.5 + j2.5 ohms and 8.6 + j2.5 ohms, respectively. Determine the value of the starting capacitance that will place the main and auxiliary winding currents 90ยฐ apart at starting,

A.ย  186.75 ฮผF

B.ย  174.35 ฮผF

C.ย  182.43 ฮผF

D.ย  170.67 ฮผF

Solution:

361.ย  EE Board Exam October 1990

Two impedances A and B are connected in parallelย across aย 120 V ac supply. The total current and the current in each impedance is adjusted to 20 A.ย  Theย power drawn by Aย is doubledย that of B andย the power factor is lagging. Determine the power factor of A.

A.ย  0.650 lagging

B.ย  0.704 lagging

C.ย  0.841 lagging

D.ย  0.677 lagging

Solution:

362.ย  REE Board Exam March 1998

A coil of 50-ohm resistance and of 150-mHย inductance is connected in parallel with aย 50-ฮผFย capacitor.ย Ifย the sourceย voltage is 100ย sin (ฯt + 30ยฐ), what is the equation of the line current?

A.ย  1.91 sin (ฯt + 52.5ยฐ)

B.ย  1.25 sin (ฯt + 75.5ยฐ)

C.ย  1.82 sin (ฯt – 62ยฐ)

D.ย  1.32 sin (ฯt โ 75.5ยฐ)

Solution:

363.ย  EE Board Exam October 1984

A resistor R is connected in parallel with a 10-ohm inductive reactance. The combination is then connected in series with a 4-ohm capacitive reactance. The whole combination is connected across a 100-volt, 60 Hz supply, How much is R if the angle between the supply voltage and the total current is 45 degrees?

A.ย  12 ohms

B.ย  25 ohms

C.ย  16 ohms

D.ย  20 ohms

Solution:

364.ย  EE Board Exam April 1980

Three impedances Z1 = 1 – j4 ohms, Z2 = โ j6 ohms and Z3 = 4 + j3 ohms are connectedย  inย  series-parallel.ย  Z1ย  isย  connectedย  inย  seriesย  withย  theย  parallel combinationย  ofย  Z2ย  andย  Z3.ย  Determineย  theย  equivalentย  impedanceย  ofย  the combination.

A.ย  4.32 โ j1.21 ohms

B.ย  2.23 โ j3.32 ohms

C.ย  6.76 โ j5.68 ohms

D.ย  5.42 โ j7.21 ohms

Solution:

365.ย  EE Board Exam October 1984

A 5-ohm resistor is connected in parallel with a 10-ohm inductive reactance. The combination is then connected in seriesย withย aย  4-ohmย  capacitive reactance. The whole combination is connectedย acrossย aย 100-volt,ย 60 Hz supply. How much is the total current drawn by the circuit?

A.ย  22.36 A

B.ย  20.45 A

C.ย  23.16 A

D.ย  19.89 A

Solution:

366.ย  EE Board Exam April 1983

A non-inductive resistor R is connected in parallel with an inductive reactance of 10 ohms.ย The combination isย then connected in seriesย with a capacitive reactance of 5 ohms. The whole combination is connected across aย  100-volt,ย  60ย  Hz ac source. If R is equal toย 5 ohms, solveย for the voltage across the parallel combination.

A.ย  87.53 V

B.ย  88.34 V

C.ย  89.44 V

D.ย  91.87 V

Solution:

367.ย  EE Board Exam April 1980

Three impedances Z1ย  = 1ย  –ย  j4 ohms, Z2ย  =ย  โย  j6 ohms and Z3ย  = 4 + j3 ohms respectively are connected in series-parallel. Z1ย  is connected in series with the parallel combination of Z2 and Z3. If this circuit is connected across a 230 V, 60 Hz source, determine the voltage across the parallel combination of Z2 and Z3.

A.ย  156.3 V

B.ย  146.8 V

C.ย  135.7 V

D.ย  163.2 V

Solution:

368.ย  EE Board Exam October 1980

Given three impedances: Z1 = 10 + j0 ohms, Z2 = 3 + j4 ohms and Z3 = 8 โ j6 ohms. Impedance Z2 and Z3 are connected in parallel and the combination is connected in series with impedance Z1 across a 120 V single-phase 60 Hz source. Find the total power drawn by the impedance.

A.ย  1008 W

B.ย  1204 W

C.ย  1038 W

D.ย  1103 W

Solution:

369.ย  EE Board Exam October 1993

If admittance Y = 0.06 โ j0.08 mho, then conductance G equals

A.ย  -0.06

B.ย  0.06

C.ย  0.08

D.ย  -0.08

Solution:

Given that admittance Y=0.06โj0.08 mho, conductance G can be calculated using the formula:

G = Real part of admittance

G=Real(Y) = 0.06 mho

370.ย  EE October 1986, April 1993

A parallel circuit consists of a resistor having a conductance of 4 mhos, an inductive reactor having a susceptance of 8 mhos and a capacitive reactor having a susceptance of 5 mhos. What is the impedance of the circuit?

A.ย  0.11 + j0.13 ohms

B.ย  0.13 + j0.11 ohms

C.ย  0.12 + j0.16 ohms

D.ย  0.16 + j0.12 ohms

Solution:

371.ย  REE Board Exam October 1994

A capacitor branch having a ratio of XC to R of 5 is paralleled with impedance consistingย  ofย  aย  4ย  ฮฉย  resistanceย  andย  aย  3ย  ฮฉย  inductiveย  reactance.ย  Theย  power factor of the resulting circuit is 0.8 leading. Find the size of the capacitor in ฮผF if the frequency is 60 Hz.

A.ย  879.9 ฮผF

B.ย  1078.9 ฮผF

C.ย  978.9 ฮผF

D.ย  778.9 ฮผF

Solution:

372.ย  ECE Board Exam November 2000

A parallel-LC circuit can store energy fed to it power source and produces an output which is a continuous A.C. wave. It is often called a ____.

A.ย  Tank circuit

B.ย  Store circuit

C.ย  Storage circuit

D.ย  Power circuit

Solution:

373.ย  ECE Board Exam November 2001

What is the impedance relationship between the output of one circuit and the input of another circuit will provide maximum power transfer?

A.ย  very low impedance

B.ย  higher impedance

C.ย  lower impedance

D.ย  equal impedance

Solution:

374.ย  The series circuit of R = 30ย  ฮฉย  & X = 4ย  ฮฉย  and a parallel circuit of Rโ and Xโ have the same impedance and power factor. Calculate the value of Rโ and Xโ.

A.ย  8.33 ฮฉ and 6.25 ฮฉ

B.ย  2.56 ฮฉ and, 3.83 ฮฉ

C.ย  7.47 ฮฉ and 7.51 ฮฉ

D.ย  5.62 ฮฉ and 9.84 ฮฉ

Solution:

375.ย  A 25 ฮฉ resistor, 2 mH inductor and 30 ฮผF capacitor are connected in parallel across 100 sin (5000t + 45ยฐ) V source. Calculate the total current taken by the circuit.

A.ย  4 sin (5000t + 45ยฐ) + 5 cos (5000t + 45ยฐ)

B.ย  14 sin (5000t) + 15 sin (5000t + 45ยฐ)

C.ย  40 sin (5000t + 30ยฐ) + 50 cos (5000t + 45ยฐ)

D.ย  4 cos (5000t + 45ยฐ) + 5 cos (5000t + 45ยฐ)

Solution:

376.ย  A parallel circuit with one branch of R = 5 ฮฉ and a single unknown element in the other branch has the following applied voltage and total current e = 10 cos (50t + 60ยฐ)ย  V and i = 5.38 cos (50tย  โย  8.23ยฐ) A. The unknown element is ______.

A.ย  L = 0.04 H

B.ย  L = 0.02 H

C.ย  C = 10 ฮผF

D.ย  C = 5 ฮผF

Solution:

377.ย  An impedance of 3 โ j3 ฮฉ is connected in parallel with 5 + j2 ฮฉ. The voltmeter connected across 3ย  ฮฉย  resistance measures 45 V. Calculateย  the total current of the circuit.

A.ย  22.4 A

B.ย  41.3 A

C.ย  13.4 A

D.ย  7.91 A

Solution:

378.ย  Twoย  impedancesย  ZAย  =ย  4ย  +ย  j6ย  ฮฉย  andย  ZBย  areย  connectedย  inย  parallel.ย  The apparentย  powerย  forย  theย  impedanceย  Bย  isย  1490ย  VA.ย  Determineย  theย  total apparent power.

A.ย  4250 VA

B.ย  3290 VA

C.ย  2652 VA

D.ย  8031 VA

Solution:

379.ย  Aย  feederย  suppliesย  twoย  loads,ย  oneย  atย  50ย  amperesย  atย  50%ย  powerย  factor,ย  the otherย  150ย  amperesย  atย  unityย  powerย  factor.ย  Theย  total currentย  suppliedย  byย  the feeder is approximately ____.

A.ย  180 A

B.ย  200 A

C.ย  175 A

D.ย  150 A

Solution:

380.ย  Aย fluorescent lampย and its inductiveย ballastย draw a 1.0 A currentย atย 50% lagging power factor from a 120-V, 60-Hz source. What is the overall power factor when a 26.5 ฮผF capacitor is connected across the fixture?

A.ย  0.832 lagging

D.ย  0.5 lagging

Solution:

381.ย  Ten impedances connected in parallel draw the following individual current: 5โ 0ยฐ,ย  5โ 5ยฐ, 5โ 10ยฐ,ย  5โ 15ยฐ, 5โ 20ยฐ, 5โ 25ยฐ, 5โ 30ยฐ, 5โ 35ยฐ, 5โ 40ยฐ, 5โ 45ยฐ. What is the effective value of the total current?

A.ย  48.444 A

B.ย  34.255 A

C.ย  25.345 A

D.ย  84.389 A

Solution:

382.ย  Ten impedances connected in parallel draw the following individual current: 5โ 0ยฐ,ย  5โ 5ยฐ, 5โ 10ยฐ,ย  5โ 15ยฐ, 5โ 20ยฐ, 5โ 25ยฐ, 5โ 30ยฐ, 5โ 35ยฐ, 5โ 40ยฐ, 5โ 45ยฐ. What is the equivalent impedance that could replace the impedances if the source voltage is 100 sin 150t V?

A.ย  1.325โ -30ยฐ ฮฉ

B. 6.026โ -2.5ยฐ ฮฉ

C.ย  32.51โ 50ยฐ ฮฉ

D. 1.46โ -22,5ยฐ ฮฉ

Solution:

383.ย  Ten impedances connected in parallel draw the following individual current:ย 5โ 0ยฐ,ย  5โ 5ยฐ, 5โ 10ยฐ,ย  5โ 15ยฐ, 5โ 20ยฐ, 5โ 25ยฐ, 5โ 30ยฐ, 5โ 35ยฐ, 5โ 40ยฐ, 5โ 45ยฐ. What is the equivalent power factor of the circuit?

A.ย  0.924

B.ย  0.866

C.ย  0.707

D.ย  0.876

Solution:

384.ย  Ten impedances connected in parallel draw the following individual current: 5โ 0ยฐ,ย  5โ 5ยฐ, 5โ 10ยฐ,ย  5โ 15ยฐ, 5โ 20ยฐ, 5โ 25ยฐ, 5โ 30ยฐ, 5โ 35ยฐ, 5โ 40ยฐ, 5โ 45ยฐ. What element should be connected across the circuitย  so that the current would be in phase with the source?

A.ย  54 mH

B.ย  25.4 mH

C.ย  13 mH

D.ย  31 mH

Solution:

385.ย  A small single-phase, 240 V induction motor is tested in parallel with 160ย  ฮฉ resistor. The motor takes 2 amperes and the total current is 3 amperes. What is the power of the whole circuit?

A.ย  800 W

B.ย  360 W

C.ย  220 W

D.ย  580 W

Solution:

386.ย  A capacitor is placed in parallel with two inductive loads, one of 20 A at 30ยฐ lagging and another of 40 A at 60ยฐ lagging. What current in amperes should flow in the capacitor so that the circuit will have a unity power factor?

A.ย  35.8 A

B.ย  44.6 A

C.ย  28.8 A

D.ย  50.2 A

Solution:

387.ย  A coil of 10 ฮฉ resistance and 0.1 H inductance is connected in parallel with a capacitor of unknown capacitance. If the total impedance of the combination is 100 ฮฉ, determine the value of the capacitance.

A.ย  50 ฮผF

B.ย  100 ฮผF

C.ย  150 ฮผF

D.ย  200 ฮผF

Solution:

388.ย  An impedance equal to 4.44โ 60ยฐ ฮฉ is connected across a 220 V source. What should be the value of the second impedance in parallel with the first, if the total power delivered to the circuit is to be 16.5ย kWย and the overall power factor is to be unity?

A.ย 2.21โ 30.1ยฐ ฮฉ

B.ย 3.33โ -40.9ยฐ ฮฉ

C. 5.63โ 30ยฐ ฮฉ

D.ย 6.543โ -45ยฐ ฮฉ

Solution:

389.ย  Anย inductive reactance of 8 ohms is connected in parallel with a capacitive reactance of 18 ohms. This combination is then connected in series with a variableย resistance.ย For what value ofย resistance willย the power factor be 0.5?

A.ย  8.314 ฮฉ

B.ย  3.318 ฮฉ

C.ย  13.81 ฮฉ

D.ย  1.381 ฮฉ

Solution:

390.ย  Twoย impedances Z1 =ย 3 + j4 and Z2 = 5 โ j8.66 ohms respectively are connected inย parallel.ย  Ifย theย combination isย connectedย acrossย aย 240 Vย AC source, how much is the total current?

A.ย  44.4 A

B.ย  42.1 A

C.ย  40.6 A

D.ย  39.9 A

Solution:

391.ย A resistance of 20 ohms and an unknown capacitanceย are connectedย in parallel across a 110 V, variable frequency AC source. When the frequency is 60 Hz, the current drawn by the circuit is 6 A. At what frequency will the current drawn fall to 5.8 A?

A.ย  42. 33 Hz

B.ย  50.12 Hz

C.ย  46.02 Hz

D.ย  44.18 Hz

Solution:

392.ย  Two parallel branches have admittances 0.3 +ย j0.4 and 0.2 โ j0.25ย S, respectively.ย If the current in the first branch is 10ย A,ย determine theย total current supplied to the parallel combination.

A.ย  10.44 A

B.ย  12.10 A

C.ย  15.32 A

D.ย  11.24 A

Solution:

393.ย  An inductive reactance of 3 ohms is connected in parallel with a capacitive reactance of 4 ohms. If the combination is connected in series with a 4 ohm resistance, solve for the power factor of the whole combination.

A.ย  0.333

B.ย  0.409

C.ย  0.567

D.ย  0.316

Solution:

394.ย  An R-L circuit has Z = (6 + j8) ohm. Its susceptance is ____ siemens.

A.ย  0.06

B.ย  0.08

C.ย  0.1

D.ย  -0.08

Solution:

395.ย The impedances of two parallel branches of a circuit are (10 + j10) and (10 โ j10) respectively. The impedance of the parallel combination is

A.ย  20 + j0

B.ย  5 โ j5

C.ย  10 + j0

D.ย  0 โ j20

Solution:

396.ย  Domestic appliances are connected in parallel across ac mains because

A.ย  it is a simple arrangement

B.ย  operation of each appliance becomes independent of each other

C.ย  appliances have same current ratings

D.ย  this arrangement occupies less space

Solution:

397.ย  Whenย  aย  parallelย  acย  circuitย  containsย  aย  numberย  ofย  branches,ย  thenย  itย  is convenient to solve the circuit by

A.ย  phasor diagram

B.ย  phasor algebra

C.ย  equivalent impedance method

D.ย  none of the above

Solution:

398.ย  The power taken by the circuit shown in Fig. 13.1 is

A.ย  470 W

B.ย  1920 W

C.ย  1200 W

D.ย  none of these

Solution:

399.ย  The active component of line current in Fig. 13.1 is

A.ย  8 A

B.ย  4 A

C.ย  5.3 A

D.ย  none of these

Solution:

400.ย  The power factor of the circuit shown in Fig. 13.1 is

A.ย  0.707 lagging

B.ย  0.5 lagging

C.ย  0.866 lagging

D.ย  none of these

Solution:

#### Questions and Answers in AC Circuits

Following is the list of practice exam test questions in this brand new series:

MCQ in AC Circuits
PART 1: MCQ from Number 1 โ 50                  Answer key: included
PART 2: MCQ from Number 51 โ 100              Answer key: included
PART 3: MCQ from Number 101 โ 150            Answer key: included
PART 4: MCQ from Number 151 โ 200            Answer key: included
PART 5: MCQ from Number 201 โ 250             Answer key: included
PART 6: MCQ from Number 251 โ 300             Answer key: included
PART 7: MCQ from Number 301 โ 350             Answer key: included
PART 8: MCQ from Number 351 โ 400             Answer key: included
PART 9: MCQ from Number 401 โ 450             Answer key: included
PART 10: MCQ from Number 451 โ 500           Answer key: included

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