Dc Circuits 4j6l3d

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DIRECT

CURRENT CIRCUITS : PART-I

I 1.

RESISTANCE /NETWORK THEOREMS

[,,

II !;

· RESISTANCE ( R ): It may be defined as that property of a substance or material which opposes the flow of electron or current.

I''

i li

The Resistance o(a conductor is given bv: l 12 v R=p-=p-=pA V A2

!j

Where : l =length of the conductor in m or ft. A = cross sectional area in m 2 , sq. mils or circular mils (CM).

' I

A== !!...d 2 sq. mils; A ::d 2 CM; if d =diameter ofthe conductox in mils. 4 6 6 NOTE: 1 inch== 1000 mils, 1 sq. inch= 10 sq. mils, 1 sq. x 10 CM

inch=~rr

p =specific resistance or resistivity of the material of the conductor in Q-m or 0-CM/ft. = 1.77 x 10-& 0-m =10.66 0-CM/ ft => for hard-drawn Coppe1 (HDC)@ 20°C = 1.72 X 10 78 Q-m =10.50 n-CM/ ft => for annealed Copper@ 20 "C = 2.83 x 10 --& Q-m = 17.10 Q-C!V'J ft => for Aluminum @ 20 °C 3 3 V = volume of conductor in m or ft •

,,'

II ~~ ~~

li

Where: R =_resistance@ t 2 ,

final value of resistance in Q

2

R =resistance @

!'

1

·,

t

'I

I

1

initial value of resistance in Q

1 , 1

,r 2 =initial and final temperature in oc respectively.

al =temperature coefficient @ tl in oc-t

T ""' - 1- = inferred absolute zero resistance temperature in °C. ao .

;I

T = -234.5 °C for annealed copper, T = -242

II IIii

oc for HDC, T = -23o oc for aluminum.

OHM'S LAW : it is stated that thi: ratio of potential difference (V) between any two points on a conductor to the current (I) flowing between them, is constant provided the temperature of the conductor

iiI

!l ji:

does not c h ange.

li

V R . V t.e. - "" constant or - == I I

1:

:!'

RESISJ ANCE in PARALLEL : I l I

RESISTANCE in SEIUES :

I

- = - + - + - + ... + -

RT R1 R 2 R 3 Vr =VI =V:= v.~ =··· lr = I 1 ·t/ 2 1 / 3 t .. · 1

i

I· !

'I

II

Vr =V1 +V1 + V3 + ... +V,

l'i

,'

1r

=//=h""fJ=···=JII

1

i·i

:jI' ~~

I~ l:

,,

'l l ··,!

!

1'

1

1

1

v. / 11

Gr = G1 + G2 + GJ + ... + G"

1

- = - + - + - + ... + Gr Gl Gz GJ G" where : G

R11

=

conductance in mho

n·l

l

,.

. /

. 1

'·

WORK, POWER and ENERGY: Joule's Law of Electric Heating is the amount work required to maintain a current I amperes through a resisiance R ohms fort seconds is given by : 2 v2t W =I Rt = Vll = - - = Pt in Joules R This work is convertf!d into heat and is dissipated away, the amount of heat produced is given by: work. Q =- - m kcal or BTU J Where : J =mechanical equivalent of heat =4.186 KJ I kcal = 778.16 ft-lb/ BTU 7 NOTE : 1 Joule = 10 ergs = 0.24 gm-calorie , l erg= 1 dyne -em

THERMAL EFFICIENCY : lt is the ratio of the heat actually utilized to the total heat produced electrically. Hence, the relation between heat produced electrically and the heat absorbed usefully becomes :

VIt --17 J

'~

where : 17 = thermal efficiency, m = mass in gm.,

' mV•;r)

=specific heat constant in cal./ gm- "C L\T

=

change in Temperature in "C

NETWORK DEFINITIONS : CIRCUIT -is a conducting path through which either an electric current" flows or is intended to flow. PARAMETERS- it is various elements of an electric circuits such as Resistance. Inductance and capacitance. These may be Lumped or Distributed. LINEAR CIRCUIT- a circuit one whose parameters are constant i.e. do not change with voltage or current. NON-LiNEAR CIRCUIT- a circuit one whose parameters change with voltage and current. UNILATERAL CIRCUIT- it is that circuit whose properties changes with the direction of its operations. A vacuum tube rectifier is a unilateral circuit. BILATERAL CIRCUIT- a circuit having identical properties in either direction. Transmission line is a bilateral circuit. ACTIVE NETWORK- a network containing one or more sources of e.m.f. IVE NETWORK- a network containing no source of e.m.f. IDEAL CONSTANT- VOLTAGE SOURCE- is that voltage source whose output vol!age remains absolutely constant whatever the change in load current. Such a voltage source must possess zero resistance so that internal voltage drop in the ,\'OIIrce is zero. IDEAL CONSTANT- CURRENTS'OURCE- is that voltage source whose internal resistance is · ·---infinity. In practice, it is approached by a source which possesses very high resistance as compared to that of the external load resistance.

FARADAY'S LAW OF ELECTROLYSIS; 1

1• • Law:

m=zit=(~.;)It

2"d. Law: ~ "' ..:L m2

z2

where : m = mass of ions liberated in gms. a== atomic wt. of the substance. F =Faraday's riumber ==

Chemical

z = electro-chemical equivalent wt.in gm I coul. v = valency of the substance.

equivalent

Electrochemical

equivalent

96,485 Coull gm

~

equivalent

PAR T J.VI_A...GNETIC FIELD

&

II INDUCTANCE:

MAG.'VETJC FIELD: exists in a region of space if a moving charge there experiences a force (other than · Friction ) due to its motion. Tile Magnitude o(F£Jrte is given hv: F "" qvB sin 8 . in Newton. where : q = the charge magnitude in coul. ( C ), v = the magnitude of the velocity in m/sec. 8= the angle between the field lines and the velocity. B = magnetic flux density or magnetic induction in Tesla ( \Vb/m2 ) NOTE : 1 Tesla = 10 4 Gauss= 10 4 lines/cm 2 = 1 N/A-m

Force 011 a Current in a Magnetic Field is : In metric: F == B!Lsin8 in Newton where : B =magnetic induction, Tesla 1 = cunent in Amp L = length of conductor, m 8= angle between the direction of 1 and B. {J!/,sin (} lu CUS • F in dynes lO

where : 8

=

in Gauss,

In English : where : B =in lines/in 2 ,

rl I !

!=in Amp, F = JJ/LsinO 11,300,000 /=in Amp,

L =in em

in lbs.

L= in inches

Torque on a Flat Coil in fl Uui(Orm Mag11etic Field is : r = N!ABsin8 in N-m where : N =number of loops or turns, A =area of the coil, m 2 0 ".angle between Band perpendicular to the plane of the coii NOTE : To determine the direction of rotation of the coil use Right- Hand Ruie. Magnetic Field 011 a Lo11g straight wire :

Pol B=2m·

where : r is the distance to a point from the axis of the wire.

Maguetic Field 011 Center o(a Circular coil with N loops:

B = PoNI 2a

where: a i:; the radius of the circular coil.

Magnetic Field bt tlte Interior IJOillt o(a Long Solenoid:

B = Po nl

where : n is the number of turns per meter = N .

f

Magnetic Field iu the interior poillt of Toroid witlr N loops: PoNI B =- - where : r is the radius of the circle on which a point lies. 21(!' Force betwee11 Two Parallel CoJtductors: F = p

01112

21Cd

e == 2xl 0 -? f/d2 f.

where :

e is the length of the conductor, and d is the distance between conductors

,,,,'I

Coulomb's Law o(Magnetic Forces: F =

1

47[/..lof.lr

M M2

where : M 1 & M 2 are pole strength in Wb., and

r2

r is the distance between the poles, m.

Faradav's Law o(Electromaglletic lllductioll (eqt'lls. o(luduced emO:

le! == Nl/!.¢1 =LIM!= Rl!!.ql = Bfvx w-s 6.t ' 6.t . 6.t

in volts

INDUCTANCE (L) :is the property of AC circuits which opposes any change in the amount of cmTent, Its unit is Henry. Expression o(Selflnductance : 2

- N¢ __ p,p 0 AN , H Lm enry 1 where : A =is the area of cross section of the core in rn2, ¢=is the magnetic flux in Wb,

e

e=is the length of the core in

rn

Jl, = is the relative permeability of th<:: core

Expre.vsitm o(Mulllallm/ucttmce:

M

=k~LILz

= PrJ.IoANINz in Henry

I! where : k = coefficient of coupling N 1, N2 = respective number of turns L~.L 2 =respective self- inductances of the two coils,

l11ductances i11 Series : When M assists L 1 & L 2

lmluctrmces iu Parllllel : When M assists L 1 & L2

When M opposes L 1 & L 2

LIL2 - M 2 L 1 + L 2 -2M When M opposes L 1 & L 2 L"'

L=

LIL2 -M2

L 1 +L1

+2M

Ohm's Law of Magnetic Circuits :

¢ = m.m.f. 91

= Nl = 9l

·

= f.lrf-loANI

Nl

P/

/ llrf.lo

A

in Weber

f'

Where : 9i =is the Reluctance of the magnetic circuit, it is reciprocal of Per,neance Energy Stored in a Magnetic Field: WL=}._L/ 2

2

inJoules

Energy Stored in a Magnetic Field per unit Volume:. 82 3 WL

=---

in Joules/ m

2f.lof-lr

' Steinmetz's Emperical Law for ffvsteresis lfJss: . watts W, :::;-!}BmJ.6fv ill

Where : 11 =Steinmetz's coefficient in J/m 3 Bm = maximum flux density in Wb/ni

f= frequency in cycles/sec \Hz) v =volume of the core in m

PART

III

ELECTROSTATICS., CAPACITANCE INSTR.U:rv:IENT A TIONS:

&

ELECTROSTATICS: is the study of the behavior of static-electricity (i.e. electric charges which are at rest). Cou/(}mh 'sLaw o(Electro.~tatics:

F=--l_Q1Q 2 =9x10 9 Q1 Q2 47rl>oSr d 2 &,d 2

!I !II~

in Newton

Where : F = the force attraction or repulsion between two charges. Q I> Q 2 =are the respective charges in coulomb (C) NOTE: 1 Statcoul. = 3.3356 x 10 -!~ Coul. d =distance between the two charges in meters (m) s 0 = permitivity of free space or vacuum= 8.854 x 10- 12 F/m s, =relative permitivity of the medium =1.0 (for air)

'I

,.i!:

Electric Field Strength at anv point within an Electric Field : F 9 Q in N/C or Volts/m E = - =9x10 - 2

!'

Q

e,d

Electric Potential at a point lying in an Electric Field : V = work

= 9x10 9 JL

in J/C or Volts

c,d

Q

Electric Flux Deusitv of an Electric Field:

.w

.

2

D =- = e0 E,E m C/m A Where: !f!= electric flux in Coul = Q (according to Gauss's Law) A = area at which electric flux is ing normally in nl

,.I

CAPAC.1TANCE (C) : is the property of AC circuits which opposes any change in the amount of voltage. Also defined as the charge required to create a unit potential difference between its two plates. Capacitance o(a Capacitor is:

C = Q in Coul.Nolt or Farad

v

i.' i!

1:

,.

Capacitance o[an Isolated Svhere : C = 4;rs 0 err in Farad Where : r = is the radius of isolated sphere in a medium of relative permitivity s, , in m

,,I"'

Capacitance of Concentric Sphere :

I

=4;rt0 'e, .!!!!.._

(i)

with outer sphere earthed:

C

(ii)

with inner sphere earthed:

C =4trs0 sr - - in Farad

b-a

in Farad

b2

:·'1.~

,•

'

t

i l

:f

I !

b-a

Where : a and b = are the radii of two concentric sphere in m. e, =the relative permitivity of the dielectric between two spheres.

Capacitance o(Parallel Plate Capacitor: A . C = e 0 & , - 10 Farad (a) Uni'"orm dielectric. medium : 'J' d 2 Where : A =area> of each J!!iate in m , d =thickness of dielectric medium in m. & , = relat:i\(e. penniitiivity of the medium. &

r&oA

(c) Dielectric mediu.mpartlyai¥: C = r

ld- ,~-:~)

Where : d

=

air gap in m ,

]

A

in Farad

in Farad

t = thickness of dielectric medium in m

Cartacitance of. Multiple Plate Capacitor:

C.= (n-1) &ot:r~

Where : n d

= =

in Farad d number of parallel plates, A = area of each plate in m 2 separation between two plates in m, e, =relative permitivity of medium

Capacitance of Cylindrical Capacitor : C

= lr.euc,f.

in Farad

ln ro ij

Where : n0,, ri

=

outside and inside radii resp. in m, f.= length of the cable in m

9!J!.acitance in Series ; l

1

l

Capacitance iu P(fra/lel :

1

l

-=-+-+-+ooo+Cr Cl C2 C3 C,, V1 =V; +V2 +V3 +ooo+V11

Qr =- QJ

= Q2

=

C1 =C1 +C2 +C3 +ooo+C11 V1 =V1 =V2 =V3 =oooV11

Q3 = o o oQ,

Q! = Q! + Q2 + Q3 + 0 Energv Stored itl a Capacitor :

t '.

We= -CV :.:

2

2

=

l Q -QV = - in Joules 2 2C

Bnergv Stored' per VfJlume o[a dielectric metlillm : w~··

'

D2 . 3 m Joule/m 2e0 e, -

"" - -

Force o(Attraction between two plates o(parallel pl.'lte capacitor :

D2 eoe,.£2 F = -- = in N/m2

2t:0 e,.

~---·

~--~

2

0 0

+ Qll

j:

ELECTRIC INSTRUlVIENTS 2 Classes of Electric Instruments 1.

Absolute- can indicate the presence of an electric quantity. No calibration or comparison is necessary. (e.g. tangent galvanometer)

2.

Secondary- an instrument in which the value of electrical quantity to be measured can be determined from the instruments, only when they have been pre-calibrated by comparison with absolute instruments.

Types of Seco11dary I11struments 1.

Indicating instruments - displays the instantaneous values of electrical quantity on a calibrated scale. (e.g. voltmeter, ammeter, wattmeter etc.)

2.

Recording instruments- these give a continuous record of variations an electrical quantity : with respect to time. (e.g. load or demand graph, recording wattmeter etc. X

3.

or

Integrating instruments- these measure and by a set of dials and pointers. (e.g. watt-h~ur meter, Amp-hour etc.)

· Torques on ll1oviug Systems l.

Dd1ecting (operating) to1·quc- the lorce developed in an insrrument which moves the moving system of an instrument in accordance with the magnitude of the quantity to be measured.

2.

Controlling (restoring) torque- the force which controls the deflection of the pointer of an instruments and which brings the pointer back to zero. Controlling torque may be provided by spring control, gravity control.

3.

Damping torque-- torque which stops the oscillations of the pointer of an instrument. Damping can be produced by air friction, fluid friction, eddy currents.

.

I/ ....

A

j//{ji;\~ POWK.RLI!f£.

POWERLINE REVIEW cENTER

Inc.

The Ultimate E.E. Review Center

\

DC CIRCUITS

REVIEW'. PROBLEMS/QUESTIONS

1. When an electron moves because of the pressure applied to it. What is the resulting process? C. flow of current A. melting D. generating B. magnetic induction 2. Out of the following, select the best conductor of electricity? A. Polyethylene C. China Clay B. Ceramic Graphite

g

3. Which of the following con~~ctors has the highest resistance? _8 A. Manganin f"' -1-4-4~ kl1 ...tv-"'~ C. Constantan f; ~ .,._w ..JI.--""' !I- Nichrome f; 10L~ :><w'll ...fl--~"" D. Steel f ~ 'I·S ')<j«J-9..1'--""'

4. In American wire gauge as the number gage increase the wire diameter? C. does not change D. does change

A. increase

,S. decrease

5. A copper bus has a cross section of 0.5 inch x 6 inch. Calculate the area in circular mil? 6- 3,820,000 A4..;. . . "'~ Eb-S'.> )((..,(IQI>•)1 C. 382,000 8. 30,000,000 ~ct>
ii

6. A wire has a resistance of 0.75 ohm per ft at an area of 10-5 m2 . Determine the resistance of a 200ft long conductor if the area is 3 xi o-s m 2 . A. 2.5 c. 50 B: 2s 12.5

o.

7. A one-meter rod of 2 em diameter is drawn until its resistance is 100 times the initial resistance. Its length afterward is ? A. 10m B. 12.5 m

!l

t1-:. At. "' e€"'~t

C. 100m D. 5 m

fl-::.f )........ 17

8. Calculate the voltage drop in volts of a 600ft AV'vlf} circular copper conductor connected to a 100 Amp load (resistivity is 10.5 ohm-emf, area is 250,000 emil). A. 2.5 C. 5 B. 1.25 D. 2 9. A de motor draws 200 Amp is located 100 ft from the supply line. The wire has a resistance of 0.01 ohm per 100ft. What is the voltage at the motor terminals if the supply voltage is 120 Volts? ·A. 122 Volts C. 118Votts B. 124 Volts Q. 116 Volts

10. The power taken by a 500 ft resistive coil .made Volts. Resistivity_ of copper is 10.4 ohm-emil per ft. the coil in circular mil? · A. 146 C. B. 168 D.

-

of copper wire is 250 Watts at 11 0 Calculate the cross sectional area of 175 107

I

I

II,

II

:I If't

I''

1'

If

.l

I

I

"

}

11, A light bulb having a tungsten filament draws 0.5 Amp at 110 Volts. The cold resistance of the filament is 20 ohms at 20°C with temperature coefficient of resistance for tungsten at this temperature of 0.005 per °C. Determine the operating temperature of the bulb. C. 2520°C A. 1220°C D. 2020°C B. 520°C 12. A 1 00-Volt carbon filament lamp takes 1 Amp when glowing with a filament temperature of 1615°C. Calculate the momentary current when the lamp is first switched on in air temperature of 15°C. The temperature coefficient of resistance for carbon may be taken as -0.000265 per oc at 15°C. .v:: ~o-o tlo (~'h'f*'~ o.~x~ A. 1.72Amp C. 0.58Amp ""·' (mtff".,:_ ) 1 B. 0.65Amp rf

1.94Am;t~,~~_~-~~-a~,2> ~~-~€)

~ ~

13. Find the work in kWh to lift 1 ton at a height of 55 ft for 10 sec. The motor gear efficiency is 51%. A. 0.083 C. 0.83 B. 83 D. 830

-

14. A 24 Volts battery delivers 15 Amp to a motor load in 30 minutes per day. What is the energy delivered per month in kWh? A. 6.2 C. 7.31

.§. 5.4

D. 0.18

15. A certain process uses warm water at rate of 2 liters per minute. The water enters at electric heater at 25 deg C to 50 deg C. Assuming no heat losses, what is the wattage of the heater? 'Lt.. " 1.-~ A. 5125 C. 2420 (Q ... WI<- .I s. 62so o. ~ 3488 Q ~ -z.~c 1 ;;")C~,- u >oo 16. What is the watt-hour efficiency of storage battery ? A. AH output over WH input in recharge B. WH output based on WH input in recharge C. WH output based on AH input in recharge D. AH output based on AH output in recharge

lU"-

JL ... sv ~~I t..

tv"'-

I .., ~ff,O) w

...

)IC'

4-.110 '(,

Wt'rf ,..

s ~.l<'f

~ 1 VVVIi"

~.,.,

17. A 12-Volt battery has 50 Amp-hr capacity. The internal resistance is 0.1 ohm. A 5-ohm resistor is connected for 5 hours. How many Amp-hours are still left? h- 3R23 C. 41.24 B. 3 D. 11.76

18. A series loop contains the following circuit elements in order: an 8-Voit source, 2 kO resistor, a 3 kO resistor, a 16-Volt source and a 7 kQ resistor. What is the voltage across the 2 kO resistor? Source voltage are additive. A. 6 Volts C. 4 Volts B. 8 Volts 14 Volts

5.

19. Twelve resistances 1 ohm each are arranged along the edge of a cube with junctions at corners. What resistance will be measured between terminals of symJ!letrically apposite corners of the cube ? A. 6/5ohm C. 5/9ohm B. 5/6 ohm D. 6/111 ohm

20. Two-24Volt battery supply power to a 10 ohm resistance while the other has 0.4 ohm. What load draws? A. 23.84 Volts and 56.8 .Watts B. 23.68 Volts and 56.1 Watts

load. One battery has 0.2 ohm internal is the load voltage and power does this · C. 24 Volts and 48.2 Watts D. 23.24 Volts and 60.8 Watts

21. From the given network shown in Fig. 1, determine the current supplied by the 10 Volt battery and the voltage Vo. A 1.9 Amp, 12.2Volts C. -1.5 Amp, 8.8 Volts B. -2.2 Amp, -2.2 Volts D. 1.5 Amp, -8.8 Volts

20 10V

30

I

24V +

'f 12V

+

Vo

10

20 Figure 1

22. Find the current flowing in the 4-ohm resistor in the network shown Fig.2. A. -0.333 Amp C. 1.522 Amp B. 1.667 Amp D. -2.33 Amp .......

80

20 6V

Figure 2 23. A lead storage battery is rated at 12 Volts. If the internal resistance is 0.01 ohm, What is .t~,.,. a.,,.r. fD... ~-'fG'I>'i!-t" the maximum power that can be delivered to the load? A. 1,200 Watts Q.. 3,600 Watts r ~ \"' (lB. 7,200 Watts D. 1,800 Watts ~= l.]:,~rH~11'1'J ,111"1{<., h :yarv

fro;,·

i:i-zf,._~.,#

24. A steel sheet 1 m long and 30 em wide is to be plated with 0.02 mm copper. The density of copper is 8.9 gr/cm3 and its electrochemical equivalent weight is 0.3292x10-3 gm/Coul. How long should the steel sheet remain in an electroplating bath that contains copper (Cu+2 ) ions in which the current is 100 Amp? A. 541 mins. &~ 27 mins. B. 145 mins. D. 54 mins .. 25. In Flemming's Right Hand Rule, which finger point the direction of current? A. Thumb J;. Middle B. Index D. Ring

"~ c~~~~ ~K-2-')

.

26. Calculate the AT/m to produce a flux density of 0.001 Wb/sq. mts at the center of a long straight solenoid? C. 783 A. 799 D. 796 B. 745 27. A core of annealed steel sheet is wound with 1500 turns of wire through which a current of 40 rnA is flowing. If the length of the cbil is 20 em, calculate the magnetic strength is Amp-turns per meter. c. 400 A. 300 D. 450 13. 350 28. A rectangular coil of 25 loops is suspended in a field of magnetic induction of 0.2 Tesla. The plane of the coil is parallel to the direction of the field. The dimensions of the coil aie 15 em perpendicular to the field lines and 12 em parallel to them. What is the current in the coils ifthere is a torque of 5.4 Newton-meter acting on it? A. 30Amp ~ £. 60Amp B. 40Amp D. 50Amp 29. A substance or material having relative permeability of less than unity is classified as: A ferro-magnetic flr >7 o C. para-magnetic y.,.. ..111'-l-l.o 41 ·<> B. dia-magnetic )At- < t ·" D. none ofthese 30. A de current of 50 Amp flows through a long straight conductor. Determine the force on a magnetic pole of 50 unit pole strength placed 5 em from the conductor. 8. 100 dynes C. 1OOpi dynes B. 1000 dynes D. 200 dynes

31. Three phase bus bar are installed 50 em apart. The bus bars are 4 m long. On a phase to phase fault just outside the substation, the asymmetrical current carried before the bus bars is 14,000 Amperes. Determine the force between the two conductors carrying fault current? c. 65 kg b- 85 kg 6 B. 2.22 x10 dynes D. 4500 grams 32. An amperes is how many abamperes? A. 0.4 B. 0.3

C. 0.2 D. 0.1

33. A solenoid has a magnetic reluctance of 2.2 x10-3 . It has 300 turns and a core area of 5 sq. em. What is the flux density when the current flowing is 1 Amp? · A. 26,300 Gauss C. 34,200 Gauss B. 12,200 Gauss 5. 21,200 Gauss

34. A magnetic circuit consists of silicon steel of 3000 permeability and an air gap. The length of the steel core is 10 em and the air gap is 2 em both have the same· crosssection of 1.5 sq. em. A current of% Amp flows through the windings to produce 2351 Maxwell flux. How many turns are there in the coil ? """'"' · ~ -h
36. Pole strength 160 and 192 are separated by a distance. has a force of 19600 dynes. What is the distance in em? integer choices.

c. 3

&1

D. 4

B. 2

37. A current of 2 Amp through a coil sets up flux linkages of 4 Wb-turns. What is the inductance of the coil ? C. 2H A. 8H D. 1 H B. 0.5 H 38. A magnetic coil produces 100,000 maxwells with 2,000 turns and with a current of 2 Amp. The current is cut-off and the flux collapses in 0.0·1 sec. What is the average voltage that will appear across the coil ? c. 200 v A. 20 kV D. 2kV B. 2,000 kV

-

39. A 50 mH inductance carries a current of 10 Amp which reverses in 5 milliseconds. What is the average voltage induced in the inductor because of this current reversal ? A. 100 Volts C. 400 Volts B. 200 Voits D. 50 Volts 40. A metal transport plane has a wing spread of 88ft. What difference of potential exists between the extremities of the wings, when the plane moves horizontally with the speed of 150 miles per hour? The value of the vertical-component of the earth's magnetic field is 0.65 Gauss at the plane. C. 12 Volt 8. 0.12Voit D. 1.2 Volts B. 024 Volt

=

41. Two coils of inductance L1 1.16 mH, L2 =2 mH are connected in series. Find the total energy stored when the steady current is 2 Amp. A. 1.75 mJ C. 17.5 mJ B. 6.32 mJ D. 63.2 mJ 42. A non-magnetic ring having a mean diameter of 30 em the cross-section area is 4 sq. em and uniformly wound with two conductors A and B over one another. A has 90 turns and B has 240 turns. Calculate the first principle of mutual inductance between the core. C. 11.52 A. 10.62 11.00 B. 10.55

o.

43. Two coils in a network are positioned such that there is 80% coupling between them. If the inductance of one coil is 20 mH and the inductance of the other coil is 16 mH. Find the mutual inductance. ·· A. 23 mH 14.3 mH . B. 9.4 mH 5. 13.6 mH

c:

44. When two inductors are connected in series aiding, their total inductance is 40 mH, when connected series opposing the inductance is 17.5 mH. What is the value of mutual inductance? A. 0.5625 C. 56.25 B. 5.625 D. 562.5 45. Two coils of inductance 6 & 4 Henries are connected in parallel such that its coefficient of coupling is 41% with mutual inductance opposes the self-inductance. What is the total inductance of the combination ? A. 0.94 H ~- 1.43 H B. 3.33 H D. 0.49 H 46. When one coil of magnetically coupled pair has a current of-·5 Amp, the resulting flux 11 = 0.4 mWb and flux
=

47. Which has equal positive and negative charge? b._. Static charge . C. Negatively charged B. Positively charged

D. Electrically charged

48. Two charge bodies, one with + 1 0 stat-Cou! and another ~s stat-Caul allows to each other. What is the charge of each after splitting the two bodies? C. 15 stat-Coulomb A. 7.5 stat-Coulomb B. 5 stat-Coulomb .Q.,. 2.5 stat-Coulomb 49. Two equally charged spheres repel each other with a force of 0.1 kg. if their centers are 20 em apart, find the charge on each spheres. A. 1.25 x1 06 £:. 2. 00 x1 o-e · B. 3.00 x10 6 D. 2.09 x10-e

50. Three equal positive charges of 10 stat-Coulomb each are located at the vertices of an equilateral triangle of 2 em leg. What is the magnitude of the force acting on each charges? A. 12.5 dynes .,C. 43.3 dynes B. 25 dynes 0. 50 dynes 51. What will happen to an insulating medium with voltage more than breakdown voltage is applied? ,h. it will get punctured C. it will melt B. it will become magnetic D. its molecular structure will change

52. Find the capacitance of a two plate capacitor of plate area 12 sq. inch dielectric constant of 6 and dielectric thickness of 0.01 inch. A. 1.3nF C. 1.2nF ~ 1.6 nF D. 1.5 nF 53. A plate capacitor is made up of 501 sheets of aluminum 25cm x 30cm with a dielectric of paraffin paRer 0.0\115 em thick. What is the capacitance in micro-farads of the condenser (K for paraffin paper is 1.3) c.,:::. 'l.e. ."'1~ Jlllf A. 35 C. 75 B. 25 D. 50 54. A capacitor has an ii:ritial charge 8.3 Cou!. If the current flows through it is given by the equation i =2t+3 Amp, find the charge when t 1 sec. A. 16.3 Coul C. 4 Coul B. 12.3 Coul D. 6 Coul

=

-

55. A certain capacitor is charged at 48 Volts after which its energy is 5.76 x10 to negative 2 Joule. What is the capacitance of the capacitor ? A. 2 micro-farad C. 60 micro-farad B. 30 micro-farad Q. 50 micro-farad 56. Two capacitors 30 and 10 micro-farad are connected in series, what is the total capacitance? C. 20 micro-farad A. 40 micro-farad D. 300 micro-farad §_. 7,5 micro-farad 57. A capacitor is charged in 100 Volts. When it is in paralleled to 1 microfarad capacitor and the voltage is 70 Volts. What is the value of unknown capacitor in microfarad? A 2.33 C. 23.33 B. 3.33 D. 33.33 58. A 12 micro-farad capacitor charged at 500 Volts and a 6 micro-farad capacitor charged at 250 Volts are connected in parallel. What is the potential difference in the combination ? C. 750 Volts A. 500 Volts .Q. 417 Volts B. 450 Volts 59. A galvanometer has a resistance of 300 ohms. What is the ohmic resistance to make it read one is to ten? .Q., 33.33 A. 100 D. 30 B. 10 60. To roughly check his kWh meter an electrician hook-up a wattmeter, he switched on the load, he counted 5 rev in 18 sec, the meter constant is 3.2. The wattmeter reads 368 Watts. What is the error of the meter? C. 8%faster A. 8% slower Q.,_ 15% slower B. 5%faster

revprobs.Sept.20 10

DC CIRCUITS SUPPLEMENTARY PROBLEMS 1. Current has many applications in chemistry, which of the following is NOT one? A. Electrolytic diffusion C. Electroplating B. Distillation D. Battery manufacture

2. An electric current is actually a ....... . A. beta emission B. flow of electrons

C. flow of protons D. collision of molecules

3. What is the other term for American Wire Gauge? A. JIS C. DIN 8. Brown & Sharpe D. VDE 4. In metric standard, as the number of gage increase, the size ..... . A. do not change C. decrease R does change D. increase 5. What is the size in square millimeter is the cable 250 MCM size? A. 118.656 C. 112.565 8. 126.675 D. 132.348 6. A No. 14 wire (the smallest allowed in house wiring) has a diameter of 0.064 inch. Find the cross-sectionai area in drc.ular mils. A. 5000 c. 4000 §. 4096 D. 3000 7. What is the equivalent area in sq. inch for a conductor 336,400 circular mil? A. OA28 C. 0.264 8. 0.678 D. 0.768

8. A round aluminum bus bar having a cross-section of 0.185 sq. inch and a length of 2.956 ft. has a resistance of 207 micro-ohms at 20°C. What is the resistance in ohm per circular mil foot at this temperature of the aluminum bus bar? A. 18.56 ~ 16.49 B. 14.50 D. 19.00

·

9. Copper has a resistivity of 16 ohm-nm at zero degrees centigrade. What is its temperature coefficient of resistance at zero degrees centigrade? c. 4.27 x10-3 f'C A. 3.93 x1o-s f'C 3 B. 3.65 x10- FC D. 2.73 x10-3 f'C 10. A copper wire has a resistance of 2.4 ohms at 20°C. Find the resistance at 75°C. Resistance temperature coefficient at 20°C is 0.034.PC. A. 3.78 ohms C. 12.18 ohms §... 6.89 ohms D. 7.48 ohms 11. The resistance of a transformer winding is 0.25 ohm at 25°C. When operating at full load, the temperature of the winding is 75°C. The temperature coefficient of resistance for copper is 0.00427 per °C. What is the winding resistance at full load? A 0.298 ohm C. 0.512 ohm 8. 0.315 ohm D. 0.271 ohm

] 'I

'

·~~- -~~·-------·

12. What is the resistance in micro-ohms of a copper wire 100 m long and cross section of 1 cm 2 (specific resistance of copper 10.4 ohm-emf) A. 13,500 C. 17,304 B. 12,950 D. 13,970 ~

13. Calculate the voltage drop in volts of a 1000 ft AWG in gage wire connected to a 2 Amp load (rho is 10.4 ohm-emf, area is 10,380 emil) C. 3 A. 2.4 B. 1.5 D. 2

-

14. A de motor 10 hp, 230 Volts has 0.85 efficiency. The allowable voltage drop of 10% of input voltage. Find the area of wire in circular mil if the length is 150 ft and resistivity of copper is 10.4 ohm-emil per ft. A. 3088 C. 2588 D. 5176 B. 6176 15. Three resistance are connected in series has a total resistance of 120 ohms. If Rx

=20

ohms, and Ry is twice greater than Rz. Find Ry and Rz. A. Ry 75 ohms & Rz 25 ohms ~ Ry 67 ohms & Rz = 33 ohms B. Ry 60 ohms & Rz = 40 ohms D. Ry =50 ohms & Rz =50 ohms

= =

=

=

16. A certain conductor has a resistance of 1 ohm per 1000 ft at a diameter of 0.1 inch. Determine the resistance of a 200 ft long conductor if the diameter is 40 mils. C. 1.25 ohm A. 1 ohm· B. 0.8 ohm 0.5 ohm

2:

17. The resistance of a copper wire at 30"C is 50 ohms. If the temperature coefficient. of copper at O"C is 0.0042rc-1. What is the resistance at 1OO"C ? A. 72.26 ohms C. 54.25 ohms B. 63.24 ohms D. 58.15 ohms 18. The resistance of a wire is 126.48 ohms at 100°C and 100 ohms at 30"C. Determine the temperature coefficient of copper at O"C. & 0.00427 oc-1 c. o.o256 oc-11 B. 0.00615 "C-1 D. 0.0356 °C 19. Three resistors are connected in series, the impressed voltage V = 240 Volts, the resulting current I = 4 Amp, R1 = 15 ohms, R2 = 1.5 R 3 , what is R3 in ohms? ~- .18 C. 27 B. 24 D. 16 20. How many erg per second are there in one Watt? A. 10 exp 7 C. 10 exp 15 B. 10 exp 8 D. 10 exp 12 21. How much heat in kcat is produced by a current of 20 Amp flowing for one half hour in a circuit having a resistance of 6 ohms?

A 1088 B. 1032
c_

1o16 D_ 1066

at 12 Volts d.c. How many Joules does it consume in 15

c.

21,600

D.o

:I

I,· I

23. A 100 Liters of water is heated from 20°C to 40°C. How many kWhr of electricity is needed assuming no heat loss? A.. 2.3 C. 4.24 B. 5.6 D. 2.45 24. A 2.3 kWh is used to heat 100 liters of water. What is the change in temperature in degrees farenheit? A.~

c.~

B. 80

D. 20

25. Power in Watts is required to melt 10 lbs ice in 5 minutes. (Latent heat of ice is 80 Calories per gram; 1 gram-Calorie is 4.184 Joules) What is the cost of operation if power rate is Php 6.00/kWh? A. 3.05 C. 3.50 B. 6.25 D. 2.54 26.lt is a cell designed to produce electlic current and can be recharged. C. Electrolytic cell A. Secondary cell B. Chemical cell D. Battery 27. Find the current in the 3 ohm resistor of the circuit of Fig. 3 by Thevenin's theorem. A. 9 Amp C. 12 Amp B. 5.143Amp D. 6.143Amp

-

6A

60 • 36

30

v

Figure 3. 28. A 12 Volts battery of 0.05 ohm resistance and another battery of 12 Volts and 0.075 ohm resistance supply power to a 2 ohm resistor. What is the current through the load ? A. 5.85 Amp C. 5.63 Amp B. 5.72 Amp D. 5.91 Amp 29. A 25 ohm resistance and a 10 ohm resistance are connected in parallel. Then the two are connected in selies with a 5 ohms resistance. If the circuit is then connected across a 50-Volt battery with internal resistance of 0.5 ohm. What is the current flowing in the 25 ohm resistor? A. 2.83Amp C. 3.13Amp B. 3.96Amp Q. 1.13Amp 30. A circuit has resistance only. Which is CORRECT? A. Two 1000 ohm resistances in series total 707 ohms .(1. Two 1000 ohm resistances in series total2000 ohms C. A 1000 ohm resistance in series with 500 ohms total 600 ohms D. Two 1000 ohm resistances in series total1500 ohms

31. Two resistances of 10 and 15 ohms, each connected in parallel. The two are then connected in series with a 5-ohm resistance. If then connectf}d across a 12 Volt battery. What are the current and power? A. 1.2 A, 17.28 W ~ 1.09 A, 13.10 W 8. 0.96 A, 11.52 W D. 1.5 A, 20.25 W 32. A voltage source delivers 4 Amp when a load connected to it is 5 ohms and 2 Amp when the load becomes 20 ohms. What maximum power which the source can supply ? A. 180Watts C. 60Watts ~"-ltD" .,_ Y:: B. 360 Watts D. 90 Watts r.. tu ..N t_x 4~...

-

r.

ft.r-

~, fow-W' 'i'n-1-.,.., i ~

33. A coating of nickel1mm thick is to be built on a steel cylindrical shaft 20 em in diameter and 30 em in length in 2 hrs. Calculate the electrical energy used in the process if the voltage is 10 Volts, electro-chemical equivalent of nickel is 0.304x1 o-3 gram per Coulomb, specifiC gravity of nickel is 8.9. A. 13.53 kWh C. 153.3 kWh B. 15.33 kWh 0.135.3 kWh 34. A long straight conductor is carrying 100 Amp current Determine the flux density at a point 8 em from the conductor. A. 0.25 x10-3 c. 2.5 x1o-3 3 B. 0.025 x1oD. 0.25 35. F!ux of 14,000 lines has a flux density 7000 gauss, What is the area of core in sq. em? A. 1 . Q. 2 ~ .... ~ B. 3 D. 4 36. What is the magnetic: field intensity in air at a point 2 em from a long straight wire carrying a current of 5 Amp ? A. 250 A/m C. 39.8A/m B. 25 A/m D. 48.SA/m 37. A solenoid has 250 turns. What is the mmf when the current is 0.12 Amp? A. 41.2 Gilberts C. 25.1 Gilberts !l 37.7 Gilberts D. 30.0 Gilberts

38. An iron ring electromagnet having a relative permeability of 1250 when it is excited by a coil having 500 turns at 0.8 Amp. The mean length of iron parts is 48 em, the cross 2 section of core is 1o cm , and the air gap is 0.5 em. What is its total reluctance ? 3 A. 306x10 AT/ Wb ~ 4286x103 AT!Wb 3 B. 3980x10 AT/Wb D. 3674x103 AT!Wb 39. What is the heating process makes use of the currents induced by the electromagnetic action in the charge to be heated, used for hardenrng of steel. A. Dielectric heating i C. Induction heating B. Convection ! D. Infrared heating 40. The c.g.s. unrationalized unit of magnetomotiJe force is ...... A. Gilberts C. Oersted R Maxwells D. Ampere-turn

., •, •.

II

l1

41 . What is the correct induced emf ? A. Bil B. Ni/

..Q. Blv D. Bvi

-------------------------

42. The relative permeability of a certain silicon steel is 4,500. A certain magnEtic loop consist of the a silicon steel of 10 em square, 20 CITl long and an air gap of % cncWhat is the reluctance of the magnetic circuit ? A. 6.44 X 10- 4 C. 2.54 X 10- 3 3 B. 6.44 X 10D. 2.54x 10- 2 ...__ 43. A magnetomotive force is supplied by a current of 1 Amp through 100 tu·ns. The magnetic circuit consists of a steel core of 1000 permeability, 10 em long and 4 sq. em. area and an air gap of one em long. What is the field intensity at the air gap ? A. 12.25 Oersted C. 100.53 Oersted B. 497.66 Oersted D. 124.4 Oersted 44. An emf induced by the changing of current in the neighboring coil is called: A. speed C. self-induced B. mutually induced D. series 45. A south pole of 35 unit pole is placed under a south pole of 20 unit pole is 1 inch apart. What is the force between them? A. 700 dynes repulsion C. 108.5 dynes attraction B. 108.5 dynes repulsion D. 700 dynes attraction /

"-W'VU"

:j... -\"ll ~\::>.,

46. The flux density emanating from a pole of a generator is 20,000 gauss. A conductor one meter long cuts the flux perpendicularfy at a speed of 40 m per second. What voltage is developed? 8,. 80 Volts C. 230 Volts B. 800 Volts . D. 8 Volts 47. How much energy is stored in the magnetic field of a 50-millihenry coil carrying a steady current of 3 Amp? 0.225 Joule C. 0.15 Joule B. 0.45 Joule D. 0.75 Joule

a

=

=

48. Two coils having inductance L1 0.5H, L2 0.3H. At one instant, 11 == 5 A and Find the total energy stored when the coefficient of coupling isM=- 0.45H. A. 12.75 J C. 127.5 J B. 1275 J D. 1.275 J

b ==

12 A.

49. The effect of dielectric is to: A. increase the capacitance B. decrease the capacitance C. reduce the working voltage D. increase the distance between the plates

50. A conductor of active length 30 em carries a current of 100 Amp and lies at right angles to the magnetic field of strength 0.4 Wbisq m. Calculate the power develop by it if the force causes the conductor to move at a velocity of 10 m/sec. A. 119 C. 115 B. 120 D. 110 51. The conductor with length of 100 em and carrying a current of 40 Amp perpendicular to the magnetic field 1.5 Wb/sq. mts. What is the power in Watts in which the velocity is 5 m/sec? A. 3 C. 30 B. 300 D. 0.3

52. Determine the work done in moving a 50 J.LC electric charge through a distance of 50 em in the direction of a uniform electric field of 50 kVolts perm. h. 1.25 Joules C. 2.50 Joules B. 0.25 Joule D. 5.25 Joules 53. The capacitance of a capacitor formed by two parallel metal plate each of 200 sq. em in area separated by a dielectric 1 mm thick is 4.5 x10-4 micro-farad. What is the dielectric constant of the material ?

A. 3.50 B. 2.54

C. 7.50 D. 5.00

54. A condenser of 8 micro-farad capacitance is charge by connecting its plate to a 220 Volt battery, What is the charge in micro-coulomb? A. 1760 C. 1840 B. 27.5 D. 1936

55. Two condensers of 3 uF and 5 uF respectively are connected in parallel. The combination is charge with 0.0056 Caul. The charge in the 3 uF condenser is? A. 0.01 Caul .Q.. 0.0021 Caul B. 0.005 Coul D. 0.0035 Caul 56. Given a charge of 36 nCoul at time of 4 millisecond. Find the current A 9p A ' C. 0.9 rnA

-

B. 0.09 A

D. 9 A

57. A current is given by this equation i =2t3 +

f +3, a capacitor has an initial charge of 6.83 coulomb. What should be the charge of the capacitor after 5 sec? A. 362 C. 375.8 B. 385 lL 369

58. A D.C. ammeter has an internal resistance of 0.1 ohm. A shunt 1.010 x10-3 ohm is connected to the ammeter. What is t"le multiplier of the set up ?

I

I 'I

II~~ 11

A. 80 B. 100

-

C. 50 -

D. 10

59. A 200 Volt voltmeter has resistance of 80 ohm per volt. What will be the current in milli amperes if connected across a 150 Volt source? C. 115 A. 108 B. 120 Q.. 10 .,..rl-jrJ ,£·

60. In the test of a 10-Amp watthour meter having a constant of 0.4, the disk makes 40 revolutions in 53.6 sec. The average Volts and Amperes during this period are 116 Volts and 9.4 Amp. What is the error of the meter at this load ? A. 1.4 %faster ..Q.. 1.4 % slower B. 3.2 %faster D. 3.2 %slower

Practice rnakes perlect ! Supp/probs Sept. 2010

----------------