Engr. Erica Ocampo, REE ‘08

Problems in Basic

Electrical Engineering and

Safety Engineering

IEdeas Review & Training Center

CIE Examination Review Course

Electric Circuit Variables 1. Electric signals

a. Unidirectionalat- any specified time the value of the voltage or current is the same; Most commonly known as Direct Current Signal

b. Aperiodic- the waveform has no recurrence c. Periodic- the voltage or current signals recur at a regular time interval

2. Current

-the rate of flow of electrons past a given point

t

Q

dt

dqI

I=Current in Amperes (A) Q=Charge in Coulomb (C) t= time in seconds (s)

3. Potential Difference -work per unit charge necessary to bring a charge from a negatively charged plate to a positively charged plate

Q

W

dQ

dWV

W= work in Joules (J) Q= charge in Coulombs (C) V=voltage in Volts (V) Usage of E and V E= generated voltage or supply voltage V= voltage across an element or voltage between two points Voltage sources Practical Battery (DC)

E= electromotive force (emf) r=internal resistance Vt= terminal Voltage

*Primary Battery-cannot be recharged and acts only as a source *Secondary Battery- can be recharged and can act as both sources and loads

AC source The voltage or current is continuously changing as a function of time; electric charge periodically reverses direction; usually follows a sine wave

Parts of a Sine Wave a) Period is the time required for a given sine wave to complete one full cycle b) Frequency is the number of cycles that a sine wave completes in one second.

c) Peak value (Vp or Ip , Vm or Im ) of a sine wave is the value of voltage (or current) at the positive or

the negative maximum (peaks) with respect to zero. d) Peak-to-peak value (Vpp or Ipp) - voltage (or current) from the positive peak to the

negative peak. It is always twice the peak value as expressed in the following equations Vpp = 2Vp Ipp = 2Ip

e) Average value(Vave or Iave )of a sine wave is defined over a half-cycle rather than over a full cycle

mave VV

2

mave II

2

f) RMS value (Vrms or Irms ) is also referred to as the effective value. The RMS value is the equivalent heating effect of AC signal to that of DC

effmrms VVV 2

1

effmrms III 2

1

g) General equation of a wave

tYtY m sin

Where Ym=max value of the V/I

=2πf (rad/sec) =angular velocity f=frequency t=any time t(sec)

= phase angle

4. Ohm’s Law -the voltage is directly proportional to the current

IRV Where: V= voltage I= current

5. Resistance (R) -the ability of a material to limit the flow of electrons, and at the same time, convert electrical energy to other forms of energy. - unit is ohms (Ω)

Resistivity(α) • ability of a material to limit the flow of electrons • a measure of the resisting power of a specified material to the flow of an electric current. • Materials with high resistivities are used as insulators • Materials with low resistivities are used as conductors Conductivity(σ) • ability of a material to permit the flow of electrons • inverse of resistivity

A

lR

R= resistance of the conductor l = length of conductor in (m or ft) A= cross-sectional area in m2 or circular mil (CM) =d2 CM; if diameter is of the conductor is in mils

*1000 mil=1 inch

= specific resistance or resistivity of the conducting material -m or -CM/ft Effect of temperature to the resistance

)(1 12112 ttRR

α1=coefficient of temperature at t1 R1= resistance at t1 R2=resistance at t2

Voltage and current characteristics

IRV The resistance is directly proportional to the voltage and inversely proportional to the current.

Equivalent Resistance

Series

nT

nT

nT

VVVV

IIII

RRRR

...

...

...

21

21

21

n

TR

RVV 1

1

Parallel

nT

nT

nT

RRRR

IIII

VVVV

1...

111

...

...

21

21

21

eq

eq

TRR

RII

1

1 *Req is the parallel equivalent of resistors connected in parallel with R1

Three-terminal equivalent

Delta-wye

acbcab

acaban

RRR

RRR

acbcab

bcabbn

RRR

RRR

acbcab

acbccn

RRR

RRR

Wye-Delta

cn

ancncnbnbnanab

R

RRRRRRR

an

ancncnbnbnanbc

R

RRRRRRR

bn

ancncnbnbnanac

R

RRRRRRR

6. Inductor - stores energy in each magnetic field -inductance (L) unit is Henry(H)

o

L

L

X

LjfLjjX

90

2

Inductor

Series nT LLLL 21

Parallel nT LLLL

1111

21

Voltage and current characteristics

For DC The voltage across an inductor is zero and the inductor will only act as a wire

For AC

dtdi

L LV

o

L

V

L

tV

Ldt

LL

t

Vi

m

m

90sin

cos

Voltage leads the current by 90o Current lags the voltage by 90o

7. Capacitor

- stores energy in each electric field - capacitance(C) unit is Farad (F)

o

C

CfCC

X

jjjX

90

12

1

Capacitor

Series nT CCCC

1111

21

Parallel nT CCCC 21

Voltage and Current Characteristics

For DC The current through a capacitor is zero and it will act as an open circuit

For AC

Cdt

C iV

o

m

dt

tVd

dtdv

C

tCV

C

Ci

m

90sin

sin

Voltage lagss the current by 90o Current leads the voltage by 90o

8. Impedance -the opposition of current in AC circuit -the combination of resistive and reactive component of circuits

222 XRZ

jXRZ o

R

X1tan

Where Z= impedance R= resistance X=reactance Θ=impedance angle If the reactance (X) is positive, Z is inductive in nature. Else, Z is capacitive in nature

9. Power -is the time rate of expending or absorbing energy

ivdt

dq

dq

dw

dt

dwp

R

VRIVIP

22

Power in AC P=Real Power, Watts; a function of resistance, R Q=Reactive Power, VAR(Volt-Ampere-Reactance); function of reactance, X S=Apparent Power, VA (Volt-Ampere); function of impedance, Z

222 QPS

jQPS o

Power Factor Angle(θ) *phase angle difference between the voltage and current *if the power factor is lagging, the load is inductive in nature; if leading, the load is capacitive in nature; if unity, the power factor is resistive in nature

S

P

SQ

SP

P

Q

cos

sin

cos

tan 1

Real Power

cos

2

2

IV

R

V

RIP

R

R

*where cos θ is the power factor (pf)

Reactive power

sin

2

2

IV

X

V

XIQ

X

X

*where sin θ is the reactive factor (rf)

Apparent Power

IV

Z

V

ZIS

Z

Z

2

2

*IVS pf

10. Electric Energy

hrin W dtpW

Safety Engineering

• Electrical safety involves using safe practices when working with or near electricity or electrical

devices.

• This is important because electricity is dangerous.

• It can be destructive and lethal.

• It can cause shocks, burns or fire.

• Even 9-volt batteries can cause mild shocks if not handled properly

• Myth:Electricity takes the path of least resistance. This myth implies that current only takes low

resistance paths.

• Actually, current will take any path high or low resistance in order to return to the source that

provides power.

EFFECTS OF ELECTRICAL CURRENT IN THE HUMAN BODY

Current Reaction

Below 1 milli-ampere Generally not perceptible

1 milli-ampere Faint tingle

5 milli-ampere Slight shock felt. Not painful but disturbing; Average individual can let go; Strong involuntary reactions can lead to other injuries.

6–25 milli-ampere (women)

Painful shock; Loss of muscle control.

9–30 milli-ampere (men) The freezing current or “let go” range; If extensor muscles are excited by shock, the person may be thrown away; Average individual cannot let go.

50–150 milli-amperes Extreme pain; Respiratory arrest; severe muscle reactions; death possible.

1.0 Amperes and up Rhythmic pumping action of heart ceases; Muscular contraction and nerve damage occur; Death is likely.

4 Amperes and up Cardiac arrest; Severe burns; death.

Dangerous Effects of Electricity

• Shock

• Burns

• Explosions

• Fires

Fire Extinguisher Classification

Class A extinguishers are for ordinary combustible materials such as paper, wood, cardboard, and most

plastics.

Class B fires involve flammable or combustible liquids such as gasoline, kerosene, grease and oil.

Class C fires involve electrical equipment, such as appliances, wiring, circuit breakers and outlets. Never

use water to extinguish class C fires - the risk of electrical shock is far too great!

Class D fire extinguishers are commonly found in a chemical laboratory.

Class K fire extinguishers are for fires that involve cooking oils, trans-fats, or fats in cooking appliances

and are typically found in restaurant and cafeteria kitchens.

How to use a fire extinguisher

Pull the Pin at the top of the extinguisher.

Aim at the base of the fire, not the flames.

Squeeze the lever slowly. This will release the extinguishing agent in the extinguisher.

Sweep from side to side. Using a sweeping motion, move the fire extinguisher back and forth until the

fire is completely out. Operate the extinguisher from a safe distance, several feet away, and then move

towards the fire once it starts to diminish. Be sure to read the instructions on your fire extinguisher.

1. A heating coil takes 20A when a voltage of 220V is applied. Determine the resistance of the coil

a. 5.3 Ω

b. 11 Ω

c. 4 Ω

d. 7.5 Ω

2. Calculate the resistance of 100m length of wire having a uniform cross-sectional area of 0.1mm2 if

the wire is made of manganin having a resistivity of 50x10-8 Ωm

a. 400 Ω

b. 350 Ω

c. 547 Ω

d. 500 Ω

3. An aluminium wire 5m long and 2mm diameter is connected in parallel with a wire 3m long. The

total current is 4A and that in the aluminium wire is 2.5A. Find the diameter if the copper wire. The

respective resistivities of copper and aluminium are 1.7 and 2.6μΩm.

a. 1.03mm

b. 0.57mm

c. 0.97mm

d. 1.43mm

4. The filament of a tungsten light bulb has a resistance of 1Ω at 20oC. If the length of the tungsten

filament is 2cm, what should be the diameter? ρW=4.37x10-8Ωm , αW=47x10-4

a. 0.0334mm

b. 0.0874mm

c. 0.0153mm

d. 0.0684mm

5. At 30oC, a resistor is supplied 150V and receives 4A of current. What will be the temperature of the

resistor when the current has fallen to 3.25A? Assuming the voltage remains constant. α30=1/254.5

a. 75oC

b. 89oC

c. 81oC

d. 90oC

6. A platinum coil has a resistance of 3.146Ω at 40oC and 3.767Ω at 100oC. Find the resistance at 0oC.

a. 2.73Ω

b. 3.84Ω

c. 2.04Ω

d. 3.33Ω

7. The resistance in the series network (10Ω, 6Ω and 4Ω connected across a 40V source) are measured

at 30OC. Their resistive elements are made of nichrome, permanickel and grade A nickel,

respectively. What will be the resistance of the network at 60oC? αnichrome=0.00015/oC,

αpermanickel=0.0036/oC and αgrade A=0.005/oC

a. 31.40Ω

b. 19.76Ω

c. 22.35Ω

d. 21.29Ω

8. Two conductors, one of copper and the other of iron, are connected in parallel and carry equal

currents at 25oC. What proportion of current will pass through each of the temperature is raised to

100oC? The temperature coefficients of resistance at 25oC are 0.0043/oC and 0.0063/oC for copper

and iron respectively

a. 47.32% and 52.68%

b. 52.68% and 47.32%

c. 64.5% and 35.5%

d. 35.5%and 64.5%

9. Two coils connected in parallel across 100V supply mains take 10A from the line. The power

dissipated in one coil is 600W. What are the resistances of the two coils?

a. 6 and 17

b. 17 and 25

c. 10 and 6

d. 25 and 10

10. Given Vab=10V, Determine the voltage of the source.

a. 13V

b. 17V

c. 20V

d. 15V

11. What is the value of the unknown resistor if the voltage across the 500Ω resistor is 2.5V?

a. 575

b. 937

c. 233

d. 482

12. A resistor of 12 Ω is connected in series with a combination of 15 Ω and 20 Ω resistors in parallel.

When the voltage of 120V is applied across the whole circuit. Find the current taken from the supply

a. 5.83A

b. 2.55A

c. 13.42A

d. 9.03A

13. Determine the equivalent resistance of the circuit below

a. 40Ω

b. 20 Ω

c. 95Ω

d. 50Ω

14. Determine the total current

a. 7.78A

b. 8.07A

c. 7.45A

d. 6.38A

15. A practical battery can supply 5A at 15V and 10A at 12V. How much current can it supply to a 25Ω

resistor??

a. 0.287A

b. 0.924A

c. 0.703A

d. 0.687A

16. A bulb rated 110V, 60W is connected with another bulb in series, rated 110V, 100W across a 220V

mains. Calculate the resistance which should be connected in parallel with the first bulb so that both

the bulbs may take their rated power.

a. 471

b. 303

c. 294

d. 530

17. An alternating current of frequency of 60Hz has a maximum value of 120A. Write down the equation

from its instantaneous value. Reckoning time from the instant the current is zero and is becoming

positive; find the instantaneous value after 1/360 second.

a. 103.9A

b. 114.5A

c. 98.03A

d. 55.2A

18. What is the rms value of a sinusoidal alternating voltage ottv 10300sin50)( V?

a. 70.71V

b. 78.54V

c. 31.83V

d. 35.36V

19. An alternating current is represented by i=70.7sin520t. Determine the frequency and the current

0.0015sec after passing through zero.

a. 82.8Hz; 49.7A

b. 165.5Hz; 0.96A

c. 82.8Hz; 0.96A

d. 165.5Hz; 49.7A

20. If e1=A sinωt and e2=B sin (ωt-φ), then

a. e1 lags e2 by φ

b. e2 lags e1 by φ

c. e2 leads e1 by φ

d. e1 is in phase with e2

21. What is the total capacitance of a series connected capacitors :25μF, 40μF and 30μF

a. 95μF

b. 30mF

c. 10μF

d. 98mF

22. 1H, 1.5H and 0.9H inductors are connected in parallel. What is their equivalent inductance?

a. 0.29

b. 2.77

c. 3.4

d. 0.36

23. In a series circuit containing pure resistance and a pure inductance, the current and the voltage are

expressed as : i(t)=5sin(314t+2π/3) and v(t)=15sin(314t+5 π/6)

What is the impedance of the circuit?

a. 2.6Ω

b. 5.3Ω

c. 3.0Ω

d. 6.4Ω

24. Using the data from the previous problem. What is the inductance in henrys?

a. 8.34mH

b. 4.78mH

c. 5.24mH

d. 6.35mH

25. Determine the total impedance of the circuit

a. (6+j0)Ω

b. (0+j8) Ω

c. (7+j0) Ω

d. (6+j8) Ω

26. Two parallel branches A and B. Branch A has a resistance of 10Ω and an inductance of 0.1H in series.

Branch B has a resistance of 20Ω and a capacitance of 100μF in series. The source is 250V, 50Hz.

Calculate the magnitude and the phase angle of the current taken from the supply

a. 6 cis -15o

b. 8 cis 10o

c. 4 cis -13o

d. 10 cis -12o

27. The applied voltage is given by (0+j10) and the current is (0.8+j0.6)A in a series connection of

resistance and reactance. Determine the values of R and X.

a. R=6Ω and XL=8Ω

b. R=8Ω and XL=6Ω

c. R=6Ω and XL=6Ω

d. R=8Ω and XL=8Ω

28. Given: L-C-R are connected in series

L=800mH

C=5μF

R= 450Ω

V=220V, 60Hz

What is the total reactance?

a. 698.92

b. -228.92

c. -192.28

d. 228.92

29. From the previous problem, What is the total current?

a. 0.198

b. 0.388

c. 0.436

d. 0.172

30. In an alternating circuit, the impressed voltage is given by V=(100-j50) volts and the current in the

circuit is I=(3-j4)A. Determine the real and reactive power in the circuit.

a. 550W and 100VAR

b. 100W and 550VAR

c. 500W and 250VAR

d. 250W and 500VAR

31. A voltage of 200cis53o 8’ is applied across two impedances in parallel. The values of impedances are

(12+j16) and (10-j20). Determine the total VA.

a. 2500VA

b. 2000VA

c. 3000VA

d. 2870VA

32. A voltage of v(t)=141.5sin(314t-10o)V is applied to a circuit and a steady state current given by

i(t)=14.4sin(314t-20o)A is found to flow through it. Determine the power factor angle of the circuit

a. 30

b. 10

c. -30

d. -10

33. The load taken from a supply consists of (a) lamp load 10kW a unity power factor, (b) motor load of

80kVA at 0.8 power factor(lag) and (c) motor load of 40kVA at 0.7 power factor leading. Calculate

the power factor of the combined load.

a. 0.834(lag)

b. 0.899(lead)

c. 0.992(lead)

d. 0.982(lag)

34. Given VV O18300

AI O86.3487.4

What is the real power?

a. 424

b. 1461

c. 1398

d. 882

35. From the previous problem. What is the nature of the load?

a. Inductive

b. Capacitive

c. Resistive

d. None of the above

36. Given: S=853VA

Pf=0.687lagging

V=330V, 60Hz

What is the reactive power?

a. 330

b. 586

c. 620

d. 787

37. From the previous problem, What is the reactive power rating of capacitors needed to make the

power factor 0.9 lagging?

a. 27.99

b. 315.78

c. 92.59

d. 336.21

38. A coil has 50 ohms resistance and a 70 ohms reactance. A capacitor is connected in parallel to attain

a unity power factor. The source voltage is 120 volts, what is the power drawn by the circuit?

a. 162 watt

b. 97 watts

c. 132 watts

d. 52 watts

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

size of capacitor is necessary to raise the power factor to about 95%.

a. 3 KVAR

b. 2 KVAR

c. 2.5 KVAR

d. 3.5 KVAR

40. The impedances Z1 = 4+j3 ohms & Z2 = 3-j4 ohms are connected in parallel across a 220V, DC source.

What is the total current drawn by the circuit?

a. 24 A

b. 55 A

c. 48 A

d. 30 A

41. A person holds 220V bare conductor. What will be the current passing him if his resistance is 10kΩ?

a. 11mA

b. 33mA

c. 22mA

d. 44mA

42. Fire starts from under an electric post of 50kV line to ground. If the air’s resistance due to the fire

drops to 1350Ω, how much current will flow line to ground?

a. 74A

b. 12A

c. 18A

d. 37A

43. Which of the following is the fire extinguisher classification for electrical fires

a. Class A

b. Class B

c. Class C

d. Class D

44. What does PPE mean?

a. Practical Protective Equipment

b. Personal Protective Equipment

c. Protective Practical Equipment

d. Primary Protective Equipment

45. Which of the following is not an insulator

a. Wood

b. Asbestos

c. Coal

d. Graphite

46. Which of the following is used for splicing wires

a. cutter

b. snips

c. wrench

d. pliers

47. What does LOTO mean?

a. LockOut/Tagout

b. LightOff /TemperatureOut

c. LoadOff/ TimerOn

d. LockOn/TimeOut

48. Which of the following is a safe practice?

a. Electric cord under a rug

b. Permanent use of extension cord

c. Use nails to mount electric cord on the wall

d. Use the plug to unplug devices

49. Which of the following is a safe practice?

a. Use a metal ladder to fix electrical wirings

b. Tape cords to repair them

c. Ask someone to watch you

d. Wear loose clothing

50. Which of the following is not a safe practice?

a. Test tools before starting to work

b. Use one arm in working with wiring

c. Carry tools up a ladder

d. De-energize tool before working

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44. Personal Protective Equipment

45. Graphite (wood and asbestos are insulators, while not all coal are conductors. Coals are mostly

made of carbon which is a semiconductor. It can be an insulator and a conductor)

46. Pliers is used for holding and cutting

(cutter and snips are for cutting, while wrench is for tightening bolts)

47. LOTO(Lockout/Tagout) means that when a machine is under maintenance, the machine should

be locked out from the system(de-energized) and there should be a tag hanging from its main

switch that reads that it is under maintenance so that no one will turn the switch on.

48. Use the plug to unplug devices

49. Ask someone to watch you (main reason: in case of accident someone should rescue you)

50. Carry tools up a ladder