CERTC-EE Review Guide Series Review Guide Series ELECTRICAL ENGINEERING DC Circuits 1

during the next 15 sec the current is GOD BLESS J

constant at 4 amp; during a third period DC CIRCUITS (Part 1)
13. Two 30-ohm resistors are connected in of 20 sec the current decreases linearly I=
series. When a resistor R is connected to 3 amp. Determine the average current.
A. 2.2 C. 3.3 I. VOLTAGE:
across one of them, the total circuit
resistance is 40Ω. Find the ohmic value B. 2.3 D. 3.4 Energy per unit charge.
of R.
I – the current in amperes
21. Two resistors R1 and R2 in parallel has an
A. 30 Ω C. 15 Ω equivalent resistance of 10/3Ω. When a
q – the charge in coulombs
B. 45 Ω D. 10 Ω current enters the parallel circuit, it
V= t – the time in seconds
14. Determine the resistance of an alloy wire divides between the resistors in the ratio
at 900°C if its resistance is 18W at 40°C 2 to 1. Determine the R1 and R2. The electron has a charge of −1.602
and the temperature coefficient is 6.8 x A. 3 and 1.5 C. 20 and 10
B. 10 and 5 D. 15 and 7.5
V – the voltage in volts 10−19 C.
10-3 at 100°C. W – the energy in joules
22. A 12-V battery has a 50 ampere-hours
A. 343.7 W C.196.0Ω
B. 473.5 Ω D. 234.5 Ω
capacity. The internal resistance is 0.1 Q –the charge in coulombs
ohm. A 5-ohm load is connected for 5 V. THE IDEAL INDEPENDENT CURRENT
15. Three resistors with resistances 10, 20 hours. How many ampere-hours are still SOURCE:
and 50 ohms are connected in parallel left? II. THE IDEAL INDEPENDENT VOLTAGE SOURCE
across a 120-V source. What is the total This is a circuit element that
A. 28.51 C. 41.24
power? maintains a prescribed current in its
B. 38.23 D. 35.29 This is a circuit element that
A. 9,600W C. 360 W terminals regardless of the voltage
23. Four equal resistances are connected in maintains a prescribed voltage across
B. 180W D. 83.3 W across it.
parallel across a certain supply producing its terminals regardless of the current
16. Three resistors with resistances 10, 20 P power. How much power will be through it.
and 50 ohms are connected in parallel produced if the resistors are connected in
across a 120-V source. Find the power series? I
dissipated by the 10-ohm resistor. A. 16P C. 1/16 P
A. 720 W C. 1,440 W B. 4P D. 1/4 P +
B. 288 W D. 180 W
V -
24. A 12-V battery with a 0.3Ω internal
17. A storage battery which gives 32.5 Figure
resistance is to be charged from a 15-V
amperes on short circuit will supply a source. If the charging current should not
current of 7.5 amperes to a resistance of exceed 2A, what is the minimum Figure
1.2 ohms connected across its terminals. resistance of a series resistor that will VI. THE IDEAL DEPENDENT CURRENT SOURCE:
What is the emf of the battery? limit the current to this safe value?
A. 8.75 V C.11.68 V A. 1 Ω C. 2.4 Ω III. THE IDEAL DEPENDENT VOLTAGE SOURCE This is a current source in which
B. 12.24 V D. 6.5 V B. 1.8 Ω D. 1.2 Ω either a voltage or a current at some
18. A no.0000 Copper feeder, 0.46 inch in 25. A person wants to move a 20-watt FM
This is a voltage source in which other part of the circuit determines the
diameter is to be replaced by aluminum radio from a junked car with a 6-volt either a voltage or a current at some current in its terminals.
one of the same length and resistance. If battery to a new car with a 12-volt other part of the circuit determines the
the conductivity of Aluminum is 62 battery. What is the resistance of the voltage across its terminals.
percent that of copper, what will be the resistor that should be connected in
circular milage of the aluminum feeder. series with the radio to limit the current?
A. 362,330 C C. 575,000 CM
I
A. 2.4 Ω C. 1.2 Ω
+
B. 325,785 CM D. 330,625 CM B. 1.8 Ω D. 2 Ω V -
19. A 10-ohm resistor is in series with a 26. A lead wire and an iron wire are
parallel combination of two resistors of 15 connected in parallel. Their respective Figure
and 5 Ω. If the constant current in the 5- specific resistances are in the ratio of Figure
ohm resistor is 6 amperes, what total 49:24. The former carries 80 percent
power is dissipated in the three resistors? more current than the latter and the latter
A. 880watts C. 620watts is 47 percent longer than the former.
B. 320watts D. 150watts Determine the ratio of their cross-
VII. POWER AND ENERGY:
20. The current in a conductor varies as sectional areas.
follows: during the first 8 sec there is a A. 2.4 C. 2.5 IV. CURRENT: Power is the time rate of expending
linear change from zero to 4 amp; 8 B. 2.6 D. 2.7 Ø The rate of charge flow. 1 or absorbing energy.
!4
 CERTC-EE Review Guide Series Review Guide Series ELECTRICAL ENGINEERING DC Circuits 1

causes a 4-amp current to flow into B. 50 V D. 25 V

Resistivity Length Area the positive terminal? 8. A string of Christmas tree lights
ρ L A A. 13.6 V C. 12.4 V consists of eight 6-W bulbs
P= = V◌ּI B. 14.2 V D. 10.2 V connected in series is plugged into a
W-m m sq.m
2. Two resistors R1 = 3000ohms and R2 120-V outlet. What is the hot
W-cm cm sq.cm
= 4000ohms are joined in series and resistance of each bulb?
P – the power in watts W-CM/ft ft CM A. 2.4 kΩ C. 2.5 kΩ
W – the energy in joules connected to a 120-volt supply. The
voltage drop across R1 and R2 are B. 37.5 Ω D. 42.8 Ω
t –the time in seconds
measured successively by a 9. Two resistors A and B are connected
X. RECTANGULAR CONDUCTOR: voltmeter having a resistance of in series across a 120-V source.
VIII. HEAT: 50,000 ohms. What is the sum of the When a 30,000Ω voltmeter is
Energy in transit a two readings? connected across A and then across
b A. 116.02 V C. 132.5 V B, the instrument deflection is 48V in
Q = m◌ּC◌ּΔT B. 98.5 V D. 125.2 V each case. What are the ohmic
Q – heat 3. The resistance of the copper wire at values of the resistors?
Figure
m – mass 100ºC is 126.48 ohms and 100 ohms A. 24 kΩ C. 15 kΩ
C –specific heat at 30ºC. Determine the temperature B. 14 kΩ D. 18 KΩ
ΔT – change in temperature Area = a b (sq unit)
coefficient of resistance of copper at 10. Two resistors Ra=1.95Ω and
0ºC. Rb=0.05Ω are connected in parallel
1 kcal is the amount of heat required to A. 0.00427/ºC C. 0.00256/ºC and take a total of 50amp. What is
raise the temperature of 1-kg of water by B. 0.06615/ºC D. 0.00356/ºC the current through each resistor?
XI. CYLINDRICAL CONDUCTOR:
10C. 4. A heater draws 3 amperes at 12 V A. 1.25A, 48.75A C. 2.75A, 47.25A
dc. How many joules does it B. 1.75A, 48.25A D. 2A, 48A
d
consume in 10 minutes?
IX. RESISTANCE: A. 12,000 C. 720 11. A 50hp, 230-V motor operates at full
The opposition to the flow of current. B. 21,600 D. 10,800 load at an efficiency of 90 percent. It
Figure is 560 feet from a generator and the
5. The 60-W, 100-W and 200-W light wires connecting the motor and
R=ρ =ρ =ρ bulbs are connected in parallel generator are AWG#0000 wires.
Area = p/4◌ּ[d2] sq. unit across a 120-V line. Obtain the What current does the motor take?
equivalent hot resistance of the (AWG#0000 has 0.049 Ω/1000ft at
combination from the individual hot 20ºC)
where: resistances of the bulbs.
ifd is expressed in mils A. 210 A C. 94 A
R – the resistance in ohms, W A. 80 Ω C. 40 Ω B. 180 A D. 125 A
ρ– the resistivity or specific resistance of Area = d2 (CM) B. 22 Ω D. 38 Ω
12. A telegraph circuit consists of a 250-
the conductor 6. A 90-V source is in series with five Ω relay in series with the fine wires
L –the length of the conductor resistors having resistances of 4, 5, having a resistance of 50Ω. If it takes
CM = circular-mils 6, 7, and 8 ohms. Find the voltage
A – the area of the conductor 72mA to operate the relay, what
across the 6-ohm resistor. voltage must be impressed at the
V – the volume of the conductor
1 inch = 1000 mils A. 18 V C. 20 V sending end of the circuit?
B. 14.5 V D. 22 V A. 36.2 V C. 24.2 V
G= = 7. What is the maximum voltage that B. 21.6 V D. 12.8 V
can be applied across the series
combination of a 150-ohm 2-watt
resistor and a 100-ohm 1-watt Example 10:An energy of 20
G – the conductance of the conductor, Practice Problems: resistor without exceeding the power Joules is required in moving a
Siemens 2 rating of either resistor?
7
charge of 2Coulombs from point X to Y.
σ– the conductivity of the conductor 1. If a 12-V car battery has a 0.1-Ω !4
A. 24 V C. 18 V What is the potential difference between
resistance, what terminal voltage
 CERTC-EE Review Guide Series Review Guide Series ELECTRICAL ENGINEERING DC Circuits 1

Example 20: A resistor R in series Resistivity of Some Inferred Absolute Zero Temperature
X and Y? with an 8-Ω resistor and absorbs 100W Common Materials Material T (oC)
Example 11: Calculate the energy in when the two are connected across a 60- Resistivity ρ
V line. Find the unknown resistance? Material Aluminum 228
joules converted in 24 hours by a 100-W W-m W-CM/ft Annealed Copper 234.5
lamp. Example 21:Two lamps are connected in Aluminum 2.83◌ּ10-8 17.02 Hard-Drawn Copper 241.5
Example 12: The average electric-flat- series across a voltage source of 220- Copper 1.724◌ּ10-8 10.371 Iron 180
iron is rated 550W at 220V. How many volts. Lamp A has a rating 100-watts, Gold 2.44◌ּ10-8 14.676 Silver 243
disk revolutions will a watt-hour meter 110-volts, while lamp B has a rating of Iron 98◌ּ10-8 589.4
make after using it for 90 minutes 50-W, 110-volts. If the resistances of the Silver 1.629◌ּ10-8 9.805
assuming the disk makes 12rev/kWh? lamps are taken as constants, determine XIII. OHM’S LAW:
the voltage drop across lamp A. In an electrical circuit, the current is
Example 13: An electric heater draws 25 XII. EFFECT OF TEMPERATURE ON RESISTANCE
kcal in 10 minutes at 220 volts. Calculate Example 22:A resistor having a rating of OF CONDUCTORS: directly proportional to voltage and is
the current. 220-volts, 75-watts is to be connected to inversely proportional to resistance.
a 110-volts source. Calculate the power it
Example 14:An electric heater rated will draw if this resistor is connected to a
110-volts, takes 1000-watts to boil 1 liter R2 R I= I =V◌ּG
voltage source of 110-volts. R1
of water. Calculate the time in minutes
required to raise the temperature of the Example 23:Two batteries in parallel
water from 20oC to boiling. The heater supply a common load of 2 Ω. Batteries A I – current in amperes
t
has an over-all efficiency of 95%. and B have open-circuit voltages and t1 V – voltage in volts
internal resistances of 10 V, 2 Ω; and 8 t2
Example 15: If a resistor rated at 2-watts V, 2 Ω respectively. Determine the load
T R – resistance in ohms,W
and 6-volts is connected across a battery Figure G – conductance in Siemens
current.
with an open circuit voltage of 6-volts,
what is the internal resistance of the Example 24:A 30 ohms resistor is
connected in series with the parallel XIV.KIRCHHOFF’S VOLTAGE LAW (KVL)
battery if the resulting current is 0.3
ampere? combination of 150 ohms resistor and a The algebraic sum of all voltages in a
load resistor RL. The combination is circuit taken around a closed path is
Example 16: A storage battery has an connected across a voltage source of
open-circuit voltage E of 12 volts and has zero.
120-volts. Calculate the value of RL that
an internal resistance RB of 0.1Ω. will result in maximum power transferred Convention:
Calculate the terminal voltage VT if the to it. Also determine the maximum power R2 = R1 [1 + a1 (t2 - t1)]
load current IL is 20 A. (Ans. _______ ) transferred. a Path b-a:
Example 17: A 12-Ω resistor is Example 25:A series combination of two Potential Rise = +V
connected in parallel with a series V Path a-b:
resistors 1kΩ and 4 kΩ is connected to a
combination of resistors of 8 and 16 Ω. If voltage source of 100 volts. A voltmeter Potential Drop = -V
the drop across the 8-Ω resistor is 48V, b
having an internal resistance of 12 kΩ is
determine the total impressed emf. placed across the 4 kΩ resistor. What is Figure
Example 18: When two resistors are the reading of the voltmeter?
connected in series, the total resistance
R2– resistance at temperature t2 a Path b-a:
is 108Ω; when connected in parallel, the
equivalent resistance is 24Ω. What is the R1– resistance at temperature t1 R Potential Rise = +Vr
+ Path a-b:
value of each unit? T – inferred absolute zero temperature Vr Potential Drop = -Vr
Example 19: A parallel combination of 5- a1- temperature coefficient of
ohm and 20-ohm resistors is connected I
resistance at temperature t1
in series with a variable resistor and to a b
50volt source. To what ohmic value will Figure
the variable resistor be set when the
power in the 5-ohm resistor is 20 watts?

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 CERTC-EE Review Guide Series Review Guide Series ELECTRICAL ENGINEERING DC Circuits 1

XV. KIRCHHOFF’S CURRENT LAW (KCL) V = V1 + V2 + … Vn Example 1: How much current flows
through a wire if 7.488x1019 electrons
Ø The algebraic sum of all currents RT = pass a given point every minute?
entering and leaving a node is zero. The source voltage V is the summation of R1 R2 Example 2:The current in a conductor
the voltages across each resistor.
Convention: varies as follows: during the first 8 sec
Figure there is a linear change from zero to 4
RT = R1 + R2+ ..Rn amp; during the next 15 sec the current is
Current entering a constant at 4 amp; during a third period
I2 XX. SERIES-PARALLEL CIRCUIT:
I3 node: + sign of 20 sec the current decreases linearly
Current leaving a The total resistance RT is the sum of the to 3 amp. Determine the average current.
node node: - sign R1
individual resistances. RT = R1 + Example 3: How much voltage is
I1
I4 R2 R3 required to cause a current of 500mA to
flow for 2 minutes if the work done to
Figure RT = = + +.. Figure move the electron is 3kJ?
Example 4: The resistivity of a certain
conductor in SI is 0.46µΩ-m. Determine
I1 - I2 - I3 + I4 = 0 XXI. PARALLEL-SERIES CIRCUIT: its resistivity in Ω·c-mil/ft.
XVIII. RESISTANCES IN PARALLEL: Example 5:Calculate the resistance of
R2 1km long cable composed of 19 strands
IT RT= of similar copper conductors each strand
XVI. ELECTRICAL POWER: R1
Rn R3 being 1.32mm in diameter. Allow 5%
R1 R2
increase in length of the twist of each
2
P=I ◌ּR (watts) P = V◌ּI (watts) V
I1 I2 In strand in complete cable. Resistivity of
Figure copper may be taken as 1.72x10-8W-m.
Figure Example 6: A 2 meter wire of has a
P= (watts) diameter of 3 cm is stretched until its
XXII. CURRENT DIVIDER: resistance is 50 times the initial
I1 = ; I2= ; In = resistance. Calculate the new resistance
IT
I1 = Example 7: The resistance of 120
XVII. RESISTANCES IN SERIES:
meters of wire is 20-W. What is its
The same voltage V exists across each R1 R2
conductance?
V1 V2 Vn resistor. I1 I2 I2 = Example 8:A 100-m conductor has a
cross-sectional area of 2 mm2 and having
R1 R2 Rn IT = I1 + I2+ .. In Figure a resistance of 15-Ω. Calculate its
V conductivity.
I
The total current IT is the sum of XXIII. VOLTAGE DIVIDER: Example 9: The resistance of a wire is
Figure individual current passing through each 126.46 ohms at 100°C and 100 ohms at
resistor. 30°C. Determine the coefficient of the
R1 V2 = wire at 0°C.
V
I= = = GT = = + +… R2 V2

Figure
4 5
The same current I exist on each resistor XIX. TWO RESISTANCES IN PARALLEL: SAMPLE PROBLEMS: