AC Circuits

(1)

I

,j

.'

,!~1

•. ' I I~

l

i!

I I

i

1 ' , . ,,:

This Free

Quality

Manual is

Found

only

at POWERLINE

E-MAIL: [email protected]

POWERLINE REVIEW CENTER

MEZZANINE FLOOR, DONA AMPARO BUILDING CORNER ESPANA & G. M. TOLENTINO STREETS SAMPALOC, MANILA

TEL NOS. 735-73-02 & 733-21.-1.8

CEERS -·POWERLINE REVIEW CENTER

(2)

I ' ! I I .I

if'

:I

'i

I

.,

POWERLINE ENGINEERING REVIEW CENTER, .NC.

AC CIRCUIT -1 REVIEW LECTURE

Cycle-a complete change in value and direction of an alternating quantity 1 cycle "" 360 electrical degrees

Frequency (f)-no. of cycles per second (f) Hz.

Periodic time ( '[)- T@e tak(:11

to

complete one cycle

1

T "' - seconds.

f

Instantaneous value- the value of alternating quantity at any instant.

Maximum valuf!- the maximum value attained during positive or negative half cycle.

?iWYlllfl:'!ll{IUl:-"JVI!. mlflt'lne'msanitancous Values o'i'lla!1 cycle.

in general: ,.ve ... va ue-, l _ Are. a ... under ... the ... curve

-Base

. 2

Ave ... value =

-*

Max ... value

=

0.637

*

Max ... :value

For sine wave:

• 7!

Effective value-is that which wheT1 applied to a given circuit for a given time produces the same

expenditure of energy as when de is applied to the same circuit for the same

interval time.

also called "Root Mean Square" RMS value.

In general: RMS ... value = Area ... under .. .the ... square ... curve Base

l

For sine wave : RMS ... value =

J2

*

Max ... value

=

0.707

*

Max ... value RMS ... value _{1 11} ("' . )

Form factor= = . 10r sme wave

· Ave ... value

P eak actor

_fi

= Max ... . value = . 1 414 rf,· , or sme . wave )

RMS ... value

Phase DijJeJ·ence -the angular difference or angular displacement between alternating

quantities

- also called "phase angle"

Itz pltase-if twe alternating quantities attains their maximum & minimum values at the same

time.

(3)

~~ I~

I'

_,. I I

il

'., ..• ,, ,, I i:

t

·~

.f

~ 1 l I I 'l ·i

!

'

SINGLE PHASE CIRCUIT

POWER FORMULAS:

1. True, real or active power (P)

P

=

E I cos 9 = I2 R in watts.

2. Reactive or Idle power (Q)

Q = E I sine= I2 X in vars.

Where : + capacitive (or leading) vars } - inductive (or lagging) vars } 3. Apparent Power (S)

S = El ~ I2_Z₌~,_P_2_+_Q_2 _{in va}

Where :

e

= angle between E & I

Based from voltage conjugate method

DETERMINATION OF POWER (In Complex form)

1. Component method : Let E

=

E 1 + j Ez

I= I1 + j I2 2. Conjugate method:

Let E. (=conjugate ofE & I respective

P=EI

p

=

E, II+ El I2

p

a) Voltare conjugate method: S

=

E I w.r t the horizontal axis.

b.) Current Conjugate method: S = E I" w.r.t. the horizontal axis - p + j Q c-

J

p2 + Q2 UJ.!

where: + capacitive (or leading) vars - indcutive ( or lagging) vars

p I j Q '1/ p2 + Q2 L!_Q

where: - capacitive ( or leading ) vars

+ inductive ( or lagging ) vars

POWER i11 tel'ms tif MAGNITUDE:

where : p.f.

=

cos 9 P

=

I2 R = E l (p.f.) Q = 12 X 0 ' E I (r.C) S = 12 Z= E I=

J,...P_

2_+_Q_2 R P watts · = - =-=--=power factor Z S VA X Q vars . r.f. = sin

e "" -

= -

= - - = reacttve factor

Z S VA

RESONANCE

Is that condition existing in a circuit containing at least one resistor, an inductor and capacitor whete in the current behaves as if it is purely resistive.

(4)

! ,f !" I

I!

II

Characteristics o(Resonant Circuit :

1. The total current is in phase with the impressed voltage. 1. The power factor of the circuit is unity.

3. Tile tQti~cl r~~I,;~Il(;:~ p()\V~r is zero.

4. The imaginary component of the total impedance (or admittance) in complex form is zero

r I I Series Re.WJIIUIICe Ctnulithm : 1111 l~llrtlllel Re.wnumce Cmulititms:

1. XL= Xc 2. Z

=

R 3. I is maximum, Z is minimum l

=!..

R 4. I in phase with V 5. p.f. = 1.0 1. ~L =

l3c

2. Z = LIRC 3. I is minimum, Z is maximum I== VCR L 4. I is in phase with V 5. p.f.

=

1.0 RESONANCE FREQUENCY: 1. ( for series)

2. (for parallei resonant circuit)

3. (for parallel circuit)

l

Quality Factor (Q Factor)

Q

=

znf

Max ... Stored .. .Energy }

l

Energy ... Dissipated I cycle

I

Q-Zn/,L - =

_l_JL

(for series) 3 .

L1wd

---11--+o--4--+--~>

f

f.

fz

- Rs - 21fj,CRs Rs V C Q =

_!2_

== 2nf CRp

=

Rp

fL

(for parallel) 21fj,.L r

VC

Frequency at lwlfpower points I Baml-widtl! :

fi "" /,. -

4 ~L

; f2

= /,.

+

4 ~L

; BW = fz - ft =

~

f,.

Maximum Power Transfer :

(5)

J j

:I

I "' i I !' I I I

I!

li

I!

r!

I

_II

I 'I' ' ' ' 11

il

POWERLINE

REVIEW

CENTER

Inc.

The

Ultimate

E.E.

Review

Center

· A C C I R C U I T S (l<J>) R E V I E W Q U E S T I O N S

1. What is the period of a sinusoidal waveform having 1 00 MHz frequency?

fl.

10ns

C.

10 ps

B. 10ms D. 10 s

2.

What is the angular frequency of a waveform having a period of 1 msec?

b·

2000pi rad/s

C.

2000/pi rad/s

B.

1000pi rad/s D. 1000/pi rad/s

3. The complex expre~sion of voltage is 300 cis 90 deg. What is its instantaneous equation? (tM.s "'~

8-

424.4 sin (rot+90°)

C.

424.4 cos (rot+90°) B. 300 sin (rot+90°) D. 300 cos (rot+90°)

4. The instantaneous of a voltage is given as 100 sin 314t volts, What is its average value?

"lo..ve-;

II<M.y

A.

70.7 volts

C.

100 volts

B.

63.7 volts

D. 50

volts

--5.

The average value of a sinusoidal current is 100 ampere, VVhat is its rms value?

A.

63.7

A

C.

70.7

A

B.141.4A

g,.

111A

6. What is the peak factor of half-wave rectified ac?

A·

1.57 ~ 2

8.1.11 D. 1.414

7. In a pure resistive circuit, the instantaneous voltage and current are given by:

v(t)=250 sin 314t volts and i{t)= 10 sin 314t amperes. What is the average power?

A. 1250W C. 25 W

B. 2500 W D. 250 W

8. A current is represented by its equation 10 sin( rot+ 30°) and 5 sin (3rot- 30°). The magnitudes of the components are instantaneous values. What is the Rms value of the current?

A.

13.22 amperes C. 1.1 amperes B. 7.9 amperes D. 10.6 amperes

,_.

9. The power factor of the circuit is 0.8661agging. If the power input is 600 watts at a voltage of Vrms

=

110 sin{377t+10°), What is the instantaneous current?

A. 8.9 sin (377t,20°) C. 8.9 sin (377t+20°) B. 8.9 sin (377t+30°) D. 8.9 sin (377t-30°}

(6)

10.A load draws current from a voltage source. The equation of the voltage and current are 1=10 sin(rot+30°) and V=220 cos (rot-60°) What is the power?

A. 0 watt C. .J3xiOOO watts

B.

1100 watts ~- 2200 watts

11. The instantaneous voltage and current equations of an ac circuit are v(t)= 200 sin 377t volts and i(t)= 8 sin (377t-30°) amp. respectively. Determine the apparent power in complex form.

A. 296.8+j400

B.

962.8+j400

C.

692.8+j400

o.

692.8+j2oo

12. Two impedances,

Z1

= 0.8 + j5.6 and

Zz

= 8- j16 and a single-phase motor are connected in parallel across 200 Vrms, 60Hz supply. The motor draws

5 kVA

at

80% power factor

lagging.

By

current conjugate method,

find

the complex power

of impedance

Zz

? A. 4-j3

kVA

~- 1- j2 kVA

C. 6

+

j2

kVA

D.

1+ j7

kVA

13. An inductor draws

5A

of current

at

110 volts, 60 Hz. Determine the inductance.

A.

58.36 mH C. 56.38 mH

B.

53.68 mH

D.

38.56 mH

14.A

capacitor draws 2A of current

at

120

volts, 60Hz. Determine the capacitance in

micro-farad.

A

44.2

C.

36.4

B. 20.8 D. 55.6

15.A circuit has impedance of 3.464+j2.0 ohm is supplied from a source voltage of 240 volts, 60 Hz. What is the current when resistance is reduced by 50%

A. 91 A C. 72 A

B. 60A D. 54A

16.A resistance of30 ohms and an inductive reactance of 60 ohms are in series across 120 volts, 60 cycles source. Find the power factor in percent of the circuit?

8-.45 ~\.,

o{

11: C. 87

B. 67 D. 75

17.A coil connected in series with a resistance are supplied from a 240 volt 60Hz source draw 1.0 ampere current. The voltage across the series resistance and

acr~s the coil are both equal to 160 volts. Find the value of coil resistance.

A.

180

~-

20

B. 30

u.

60

18.A coil is with resistance of 1.0 ohm has an inductance of 265 mH. It is supplied from a 220 volt 60Hz source. What is the quality factor of the

coil?

Q: ~

A. 25 C.1 ~

B. 10 D. 100

(7)

-il

19.A series circuit has 50 ohm resistance, 2.22 micro-farad capacitance and inductance of 8 mH inductance. Find the total impedance at 796 Hz frequency.

A

50+j 50 C. 50.,j150

R

50-j50 D. 50 + 130

20.A series eireuit with 2 amperes flow through a 20 ohm resistor, 50 ohm inductive reactance and 60 ohm capacitive reactance. What is the supply voltage?

A.

46.9 volts C. 50.5 volts B. 40.5 volts

Q...

44.7 volts

21.A series RLC circuit is excited by a 100 volts 79.6 Hz source. Resistance R is 100 ohms, inductance

L

is 1

H

and capacitance C is 5 micro farad. Calculate the voltage across C.

A.

353.5/45°

!i

282.8/-135°

c.

70.7/-45° D. 332.6/35°

22.

A

10 ohms resistor is connected in parallel to Z=3*j4 ohms. What is the power factor?

A.

0.6

C.

0.609

B. 0.8

D. 0.809

23.A source of 100 Volts rms is supplying a resistance 80 ohms in parallel with a 200 mH inductor. To what angle is the current lag or lead?

.&

46.7 deg. lag

C. 46.7 deg. lead

B.

43.3 deg.

lag

D. 43.3

deg.

lead

24. Two impedances

Z

1=2+j4 and Z2=R+j0, are connected in parallel. Determine

R

so

that the pf of the circuit is 0.9 lagging.

~· 3.2 ohms

C.

2.4 ohms

B.

4.2 ohms D. 6.4 ohms

25.

Two impedances

Z

1=2+j3 and

Z

2=3+j6, are connected in parallel. The apparent

power of the second branch is 1490 VA. Determine the total complex power. A. 2202+j3636 C. 2562+j3122

B. 315S+j

2287

D.

3725+j

4398

26.An impedance of Z1=4+j4 ohms is connected in parallel with an impedance Z2=12+j6. 'fhe input reactive power is 2500 var lagging. What is the total active power?

A.

3025 W C. 2502 W

B. 4025 W D. 5045 W

'?.7,

A

19

C?h.m r~!?i!?tQr 99nnected in p~r~IIE)I with (lin impE)cJfl1f19El ()f

t3 -

j'?.

()hrp ~~rCJ!?!? an AC source. The entire circuit takes a total average power of 2000 Watts. What is the average power in the 15 ohm resistor

A. 2000W C. 1277W

(8)

II

11

ll

!j !' I i

28.A coil has resistance of 10 ohms and draws a current of 5A when connected across 1 00 V, 60 Hz source. Determine the reactive power

A

433 VAR C. 250VAR

B.

500 VAR

D.

300 VAR

29.A 25-kVA load with a power factor 0.80 lagging has a group of resistive heating units added at unity

power

factor. How many kW do these units takes,

if

the new overall power factor

is

Ot851agging?

A. 1.29

C.

2.4

B. 4.2 D. 2.75

30. A factory has an average demand of 1 76 kw at 70% power factor. What is the minimum size of capacitof required to raise the power factor to 95%?

~- 122 kvar

C.

165 kvar B. 82 kvar D. 157 kvar

31. A

§ingl~ ph~§~ indvQtiQn mQtQr gr~W§ 1 OA c:lt 7~% p[ Th~ VQitc:lg~ i§ '?,?.()V~ A . capacitor is 50 uF is

tnstaied

to improve power factor , What is the resulting

power factor?

A. 99%

C. 97%

B. 90% D. 95%

32. The power factor of a load on a 120 volt. 60Hz source is raised from 0.707 to 0.866 lagging by connecting a 53 micro-farad capacitor across the load. What is the true power of the load

in

watts?

A. 286 C. 862

B. 682 D. 268

33.A series circuit has 100 ohm resistance, 100 micro-henry inductance and 1 pico-farad capacitance. What is the frequency at unity power factor?

A. 18 Mhz

<;_.

16 MHz B. 14 MHz D. 12 MHz

~4.

A 100 rnH

ggil

ha§ an internal

~gyivii~l~nt r~§i§t~ng:: 9f

15

Qhms. What Piilrall~l capacitance will cause resonance at 60 Hz frequency.

A. 70 micro-farad C. 50 micro-farad

.§:

60 micro-farad D. 40 micro-farad

35.At parallel resonance, the circuit draws a current of 1

rnA.

If the Q-factor of the circuit is 100. What is the current through capacitor?

A.

2

mA

c.

1mA

B.200mA D.100mA

36. What is the dynamic impedance of a parallel resonant circuit

if

C:;: 1 pF, R;;1 ohm and L=1H?

A.

1 MQ C. 100 kQ

(9)

37.A coil of 40 ohms resistance has an inductance of 100 mH and is conn~ed in

parallel with a 30 J.t.F capacitor .What is the resonance frequency of the circuit

?

A. 23.7 Hz

C.

60Hz

B. 66.3 Hz

-

D. 79,6 Hz

.

38.A (6+j10) ohms coil is supplied by a v(t)=30 sin10t volts ac source connected in series with 12 volts battery. The internal impedance of the generator is (0.1+j2) ohms and that of the battery. is negligible. Determine the current through the coil by superposition.

~- 2.23 sin(10t-63°)+1.97 Amp.

B.

4.33 sin(10t-63°)+2 Amp.

C.

1.58 sin(10t-63°)+1.97 Amp.

D. 2.23 sin(10t+63~+1.97 Amp.

39. Obtain the thevenin's equivalent voltage at the terminal ab in the circuit shown

6,

5+j2.5 volts

C.

5 -j2.5 volts

B. 2.5+j5 volts

_sn

J. _.;:)

t-.n.:D. 2.5=j5 volts

r---\IVVIA----r--~

0. +

3.0.

40.Calculate the load impedance and the maximum power that can be transferred

across the load to

be

supplied by a 120 volts generator through a line with a total

impedance

of 12.5+j50 ohms.

A

12.5+j50 ohms & 1152 watts

B. 12.5+j50 ohms & 288 watts

C. 12.5-jSO ohms & 1152 watts D. 12.5-jSO ohms & 288 watts

(10)

i'

I [, I

I~~

I' ,. ! lj

,,

:j' '!, 'j POWER.LINE REVIE"VV C E N T E R .AC Circuit:s (1<p) Supplement:ary Problems

1. An alternating current of rectangular wave shape has an amplitude of 1 0 and a frequency of one (1). What is the average current?

~- 10 C. 5

B. 2.5 D. 0

2. The instantaneous magnitude of a voltage is given as 100 sin 377t volts; What is the rms

value of the voltage? ~'

A. 82.2 volts ~- 70.7 volts

B. 63.7 volts D. 50 volts

3. An alternating current of maximum value 20 amperes lags the reference voltage by 30

degrees. What is the magnitude of current 2 milliseconds after the current wave crosses

the

wt

axis going in the.

positive

direction?

A. 4.56 amperes B. 19.14 amperes C. D. 1 0.23 amperes 13.69 amperes

4. What is the rms value of a half wave rectified sinusoidal wave with 50 ampere amplitude?

A 25 Amp C. 50 Amp

B. 135.35 Amp D. 31.6 Amp

5. What is the average value of a half wave rectified sinusoidal wave with 70.7 ampere

amplitude?

B,.

22.5Amp

B. 135.35 Amp

C. SO Amp D. 31.6Amp

6. If a half wave rectified sine wave has an RMS value of 20 A, what is the average value ?

A. 20 Amp C. 14.14 Amp

-§._

12.74 Amp D. 28.3 Amp

7. For 381 V peak value triangular wave, the RMS voltage will be equal to ., ...

A. 100 Volts Q. 220 Volts

B. 141 Volts D. 173 Volts

8. For 184 Volts maximum value semi~circular wave, the RMS voltage will be equal to ...

&.

150 Volts C. 184 Volts

B. 141 Volts D. 163 Volts

9. A current is represented by its equation 10 sin(wt + 30 deg) and 5 sin (3rot-30 deg). The

magnitudes of the components are instantaneous values. What is the average value of the current?

A. 13.22 amperes

B. 7.9 amperes

C. 7.42 amperes

D.

1.06 amperes

10. The instantaneous value of the voltage is given by its equation v

=

105 sin wt- 25 sin 3wt

+ 15 sin (6 wt- 30 degrees). What is its Rms value?

A. 77 volts C. 105 volts

(11)

I

11. The voltages along points 1 ,2 and 3 are V 12

=

57 cis (60°) and Vz3 = 90 cis ( -30°). What is the voltage V13?

A

87 cis 15°

~

107.1 cis 2.35°

B. 63 cis 1S0 D.

112

cis 45° .

12. V12 is equal to 100 cis 30 degrees and V₂3 is equal to 50 cis 120 degrees. Evaluate V1z-Vz3·

A 62 cis 6.2 degrees

B. 127. 3 cis 39.9 degrees

g..

_{D. 62 cis (-6.2 degrees)}111.8 cis 3.4 degrees

13. A single phase circuit is supplied from a 220 volts 60 Hz source draws 2000 watts of power and 1 0 amperes current. What is

the

power factor of the circuit?

A 72.5% C. 82.6%

_.B. 90.9% D. 100%

14. A load draws current from a voltage source. The equation of current and voltage are =10 cos rot & V=220 sin rot. What is the Power?

A 0 watt

Q..

2,200 watts

B. 1556 watts 0. 1320 watts

15. The voltage and current of a load are given by their equations: V= 220 sin(rot+30°) volts and I= 10 sin(rot-30°). Determine the power factor and power.

A 86.6% lagging, 1905 watts C. 100% lagging, 2200 watts

B. 86.6% leading, 1905 watts

Q.

50% lagging, 1100 watts

16. An impedance draws a current of 10 cos (rot -30°) Amp from a voltage of 220 sin (rot+ 30°) Volts. What is the impedance of the circuit ?

A. 15.6-j15.6Q

c.

19.1-j11 Q

B. 15.6±j15.60 D. 11 ±j19.1 0

-...

17. A single phase induction motor is rated 5 hp, 75% power factor and 220-volt. What is the full load current?

A

22.5 amperes

B.

20.5 amperes C. 16.5 amperes

D. 18.5 amperes

18. The phase shift between the voltage and current vectors is due to the following loads EXCEPT one. Which one is this ?

A Magnet coils C. Electric flat iron

B. Power capacitors D. Fluorescent lamps

1~.

A VAR meter depends on the following values EXCEPT one. Which one is this?

A. voltage - C. Sine of the phase angle

B. cosine of the phase angle D. current

20. An impedance draws a current I= 10cos {rot- 30°) Amp from a voltage V = 220 sin rot

volts. What is the power ? ,

A

2200 Watts C.

19~

Watts

B. 11 00 Watts

D.

1320 Watts

21. A 50 mH inductance is connected in series with a 20 ohm resistor. If the voltage is 220

volts, what power is drawn? ·

A. 560 watts C. 802 watts

(12)

·---·---~----i' I i '\, '} !'

PO"WER..LINE REVIE"W CENTER

22. An impedance coil takes 1 0 amperes and absorbs 250 watts when connected across 220 volt, 60 Hz source. What power will it absorb when connected to 110 volt , 25 Hz mains? (BP April 1995}

A. 539W C. 239W

B.

439W

D.

339W

23. A 250 resistor is connected in series with a coil of 500 resistance and 150 mH inductance. What is the equation of the current if the source voltage is 200sin(wt-30deg)?

A. 2.16sin(rot +7°}

_§. 2.13sin(rot -67°)

C. 1.52sin(rot -67°)

D.

1.52sin(rot -30°)

24. Two relays each with 10 ohm resistance and 0.16 Henry inductance are connected in series. What is the equivalent impedance?

A. 20 +j102.2 ohms B. 20 + j95.32 ohms

.9.,

20 + j120.63 ohms

D. 10

+

j25.32 ohms

1/r.

.,Jp.-25. In a series RC circuit, the voltage across the capacitor and the resistor are 60 and 80 volt

respectively, the total voltage is _ _ _

A. 70 V g_.100V

B. 140 V D. 52.9 V

26. A coil is supplied from a 200 volt and takes a current of 2 amperes at 0. 707 power factor

lagging. The quality factor of the coil is:...._. _ _ _ _

A. 25

£.

1

B. 10 D. 100

27. A 50 and 100 microfarad capacitors are connected in series and across a 1 00 sin (wt +

30) voltage. Write the equation of the current.

A

1.2e

sin (rot

+120)

B. 1.26 sin (rot +90)

C. 5.65

sin

(rot +120)

D. 5.65 (rot +90)

28. A 160 microfarad capacitor is connected in series with a 10 ohm resistor. Write the

equation of the current when the voltag~O volts?

A. I = 9.8 sin (377 t +52 degrees) C. I

=

7.2 sin (377 t + 46 degrees)

B. I = 8.9 sin (377 t-46 degrees)

.Q.

I

=

11.4 sin (377 t + 59 degrees}

29. A 40 micro-farad capacitor is connected in series with a 40 ohm resistor. If the voltage is 220-V, what is the current?

A. 8.9 amperes

§.:_

2.84 amperes

C. 4.21 amperes D. 7.26 amperes

30. A 25 ohm resistor connected in series with a coil of 50 ohm resistance and 150 mH inductance. What is the power factor of the circuit?

A. 85%

c.

90%

,!!

80% D. 75%

31. A 40 micro-farad capacitor, 100 mH inductance and a 40 ohm resistors are connected in series. The voltage is 220 volts, what is the current?

A. 6.25 amperes C. 7.23 amperes

(13)

POVVERLINE R E V I E W C E N T E R

32. A 50 micro--farad is connected in series with a coil having 50 ohm resistance and 150 mH

inductance. The source voltage is 100 sin (rot-30°)V.

What

is the power?

A. 198watts C. 212watts .

B.

147 watts

D.

165 watts

-~.

.

, -fL

33. A coil with a measured resistance

of

10n is connected in seriesWith-a-capacitor of a

certain rating, at 60 Hz the impedance measured to be 1 O+j1 t.27 n at 30 Hz the

impedance is measured to

be

1Q-j5.7350. What the inductance Qf the ~illn millihenry?

A. 500 £.50

B. 100 0.350

34. A capacitor of 80 micro-farad is connected in parallel with 20 ohm resistor. What power is

drawn when source voltage is V=220 sin rot volts?

A 1825 watts C. 1010

watts

35. A coil of a 50 ohm resistance and of 150 mH inductance is connected in parallel with a 50 uf capacitor. What is the power factor of the circuit?

A. 80%

£..

70%

B. 50% 0. 60%

36. A coil of 50 ohm resistance and of 150 mH inductance is oonnected is parallel with a 50

micro-farad capacitor. The source voltage is 100 sin (rot +30deg). What is the equation of th~ lin~ ~urrent?

A 1.91 sin (rot+ 52.5deg)

§,. 1.25 sin (rot + 75.5deg)

C. 1.82

sin

(mt-62deg}

D. 1.32 sin {rot -75.5deg)

37. Two current, 5+j2 and 3-j2 enter a junction. What is the out going current?

A 2+j4A C. 2A

~ 8A D. 8-j4A

38. A single phase induction motor is rated 5hp, 75% power factor and 220 volts. What

approximate size of capacitor is necessary to raise the power·factor to abput 95%?

A. 3 kvar

C.

2.5 kvar

B. 2 kvar 0. 3.5 kvar

...

3~. A load of 10,000 KVA, 85% power factor lagging is connected to'S j3,200 volt line. How much reactive power is needed to correct the power factor to 97% :tagging?

A. 5,156 KVAR C. 3,138 KVAR

B. 2,547 KVAR

D.

4,753 JatAR

40. What capacitance must be placed in series with an inductamee

.of

0.05 H so that at 100

Hz, the impedance becomes equal to the ohmic resistan~?

.A

50 uF C. 35.5 uF

B. 70.7 uF 0. 87 uF

41. One

leg

of a radio tuned circuit has a capacitance of one times ten to the minus nine

farad. It is turned at 200 KHz, what is the inductance of the other leg in henry?

~· 6.33 X 10-4 C. 20 X 10-3

(14)

i

:I

I·"' I • !, ,, !

I

l l

!t

!I

ii

:I

i

I

l

_.!

l

'

).· •..

f

,I

I

_l

l

_I l J POWER.LINE R.EVIEVV C E N T E R 42. A coil of 40 ohms resistance has an inductance of 100 mH and is connected in parallel

with a 40

J,1f

capacitor .What is the resonance frequency of the circuit ?

A. 23.7 Hz C. 60Hz

B.

47.75 Hz

D.

79.6 Hz

43. A 5 mH pure inductance is connected in parallel with 1.0 f..l f capacitor. At what frequency shall the circuit be in anti-resonance.

A. 2250 hertz C. 60 hertz

B. 1020 hertz D. 100 hertz

44. A coil has a 50 ohms resistance and a 70 ohm reactance. A capacitor is connected in parallel to produce resonance. The source voltage is 120 V. What is the power drawn by the circuit.

A.

162 watts

j!.

97 watts

C. 132watts D. 52watts _

45. A 220 volts source delivers 5 amperes to a series circuit composed of 20 ohm resistor, 1 00 mH inductor and 250 microfarad capacitor, what is the source frequency in Hz?

A. 72.5

c_.

75.75

B. 60 D. 67.3

46. A 100mh pure inductance is connected in parallel with a 40 ohms resistor. V\'hat is the power drawn if the voltage is 220volts?

A 1010 watts C. 1210 watts

B. 1720 watts

D.

3018 watts

4 7. A series circuit is composed of a 100 ohm resistor and a 20 micro-farad capacitor

connected across a 240 V, 60 Hz line. Which of the following answer is WRONG

?

A. The impedance of the circuit is 167 ohms. B. Angle between the

t

and V is 53.1 degrees.

9·

The resulting current is 0.723

A

D. The voltage across the resistance is 144.6 volt

48. A series circuit is composed of j4, j6, oj9,-j2 reactances. What is the total reactance?

A. j C. j21

B. -j D. -j21A

-49. What is the reactance offered by a 100 pH inductance are connected to a 100 volt source of frequency 3MHz?

A. 767 ohm C. ~647 ohm

.§..

1885 ohm D. 1260 ohm

50. Determine the power angle in the series circuit which consist of R=25 ohms and L=0.2 H across a power supply of 200 volts, 30 Hertz.

A. 36.4deg.

B. 46.4

deg

c.

52.4deg.

(15)

,_

,, ,,

P O W E R L I N E R E V I E W C E N T E R 51. An electronic instrument that visually shows the magnitude and shape of an alternating

current signal. A. Electroscope B. Synchroscope

52. Convert 75/-26° in rectangular form.

A-

67.4-j32.9 B. 32.9-j67.4 C. Optical instrument D. Oscilloscope

c.

75-j26 D. 26-j75

53. A 120 volt, 60Hz power line voltage is applied across resistance of 10 ohms. What is the phase angie in degrees between the current and the voltage?

A.O C.45

·a. 3o

o.

15

54. A resistor of 50 ohms and an impedance of 100 +j 150 ohms are connected in parallel across 220 volts. What is the power factor of the load?

A. 96% C. 98%

B. 99% D. 95%

55. The resistor of 6 ohms and unknown impedance coil in series draw 12 Amp from a 120V, 60 Hz line. If the power taken from the line is 1152 Watts, What is the coil inductance

?

A. 15.9 mH C. 10 mH

B. 20 mH D. 1.59 mH

56. A load of 20 + j 35 ohms is connected across a 220 volts source. Determine the power

A. 1042 watts C. 596 watts

-B. 975 watts D. 1087 watts

57. A 10 ohms R1, 30 ohms XL and 60 ohms XL are connected in parallel across a 220 volts

60 Hz source. What is the current in

R1

in ampere?

A. 7.33

c.

22

B. 3.7 D. 24.6

58. What is the reactance of a 60 cycle a-c circuit containing an inductance of 1.5 H in series

with a capacitance of 40 micro farad?

-A. 499 ohms inductive C. 565 ohms inductive

B. 499 ohms capacitive D. 66.3 ohms capacitive

59. The two circuits has the following values: R₁

=5

ohms

X1=

3 ohms inductive,

R2=

7 ohms and X₂

=

4 ohms capacitive. If the terminal voltage is 120 volts., what is the total current?

A. 20.6

c.

30.8

a:

14:9

D:

35.5

60. A series circuit has R of 500 ohms, a 10 'micro-henry inductance land a 4 micro-farad

capacitance C across a 60

Hz

,120-volt power source. CompUte the load current.

A. 0.144A C. 0.120A

B. 0.100A D. 0.150A

PRACTICE MAKES PERFECTIII