DC ELECTRIC CIRCUITS - Day 5

Question 1: EE Board October 1997

     A load of 10 ohms was connected to a 12-volt battery. The current drawn was 1.18 amperes. What is the internal resistance of the battery?

A. 0.35 ohm

B. 0.20 ohm

C. 0.25 ohm

D. 0.30 ohm

Question 2:

     The potential at the terminals of the battery falls from 9 V on open circuit to 6 volts when a resistor of 10 ohms is connected across its terminals. What is the internal resistance of the battery?

A. 5Ω

B. 4Ω

C. 3Ω

D. 2Ω

  

Question 3: EE Board April 1997

     The electromotive force of a standard cell is measured with a potentiometer that gives a reading of 1. 3562 V. When a 1.0 megaohm resistor is connected across the standard cell terminals, the potentiometer reading drops to 1.3560 V. What is the internal resistance of the standard cell?

A. 174.5 ohms

B. 145.7 ohms

C. 147.5 ohms

D. 157.4 ohms

Question 4:

     A battery is formed of five cells joined in series. When the external resistance is 4 ohms, the current is 1.5 A and when the external resistance is 9 ohms, the current falls to 0.75 A. Find the internal resistance of each cell.

A. 0.5 ohm

B. 1.0 ohm

C. 0.2 ohm

D. 0.3 ohm

Question 5: EE Board April 1988

     A Barangay power station supplies 60 kW to a load over 2,500 ft, 100 mm², two-conductors copper feeder, the resistance of which is 0.078 ohm per 1000 ft. The bus bar voltage is maintained constant at 600 V. Determine the load current.

A. 105 A

B. 108 A

C. 110 A

D. 102 A

Question 6:

     A 120 V DC motor draws current of 100 A and is located 1000 ft from the supply source. If the diameter of the copper transmission line is 0.45 inch, what must be the voltage of the supply?

A. 125.32 V

B. 130.24 V

C. 129.32 V

D. 127.05 V

Question 7: EE Board October 1986

     A LRT car, 5 km distance from the Tayuman, takes 100 A over a 100 mm hard drawn copper trolley wire having a resistance of 0.270 ohm per km. The rail and ground return has a resistance of 0.06 ohm per km. If the station voltage is 750 V, what is the voltage of the car?

A. 585 V

B. 590 V

C. 585 V

D. 590 V

Question 8:

     The hot resistance of an incandescent lamp is 10 ohms and the rated voltage is 50 V. Find the series resistance required to operate the lamp from an 80 V supply.

A. 8Ω

B. 4Ω

C. 6Ω

D. 10Ω

Question 9:

A resistive coil draws 2 A at 110 V after operating for a long time. If the temperature rise is 55 ⁰C above the ambient temperature of 20 ⁰C, calculate the external resistance which must be initially connected in series with the coil to limit the current to 2 A. The temperature coefficient of the material of the coil is 0.0043 per ⁰C at 20 ⁰C.

A. 10.12 ohms

B. 10.52 ohms

C. 11.45 ohms

D. 12.05 ohms

Question 10:

A carbon resistor dissipates 60 W of power from a 120 V source at 20 ⁰C. How much power will be dissipated in the resistor at 120 ⁰C if connected across the same source? Assume the temperature coefficient of carbon at 20^thC is -0.0005 per ⁰C.

A. 61.50 W

B. 65.21 W

C. 62.34 W

D. 63.16 W

DC ELECTRIC CIRCUITS - Day 4

Question 1: EE Board April 1981, EE Board October 1984

     Two (2) 115-V incandescent lamps A and B are connected in series across a 230-V source. If lamp A is rated 75 watts and lamp B is rated 50 watts, determine the current drawn by the series connection.

A. 0.52 A

B. 0.64 A

C. 0.48 A

D. 0.57 A

Question 2:

     An arc lamp takes 10 A 50 volts. A resistance R is to be place in series so that the lamp may burn correctly from a 110 V supply. Find the power wasted in this resistor.

A. 800 watts

B. 600 watts

C. 700 watts

D. 900 watts

Question 3:

     Conductor “x” of a certain material and a given cross section has a resistance of 0.1 ohm per meter and a temperature coefficient of 0.005 per ⁰C. Conductor “y” of another material and a given cross section has a resistance of 0.5 ohms per meter and a temperature coefficient of 0.001 per ⁰C. Is desired to make a coil having a resistance of 500 ohms and a temperature coefficient of 0.002 by using suitable lengths of the two wires connected in series. Calculate the required length of wire “x”

A. 1225 m

B. 1250 m

C. 1240 m

D. 1210 m

Question 4: EE Board April 1997

     If a resistor rated at 5 watts and 6 volts are connected across a battery with an open circuit voltage of 6 volts. What is the internal resistance of the battery if the resulting current is 0.8 A?

A. 0.30 ohm

B. 0.26 ohm

C. 0.23 ohm

D. 0.03 ohm

Question 5:

     A high voltage DC transmission line delivers 1000 MW at 500 kV to an aggregate load over a distance of 900 km. Determine the voltage at the sending end. Assume the loop resistance of the line to be 1mΩ per km.

A. 510.5 kV

B. 505.2 kV

C. 507.7 kV

D. 503.6 kV

Question 6: EE Board April 1989

     It is required that a loading of 3 kW be maintained in a heating element at an initial temperature of 20 ⁰C, a voltage of 220 V is necessary for the purpose. After the element has settled down to steady state, it is found that a voltage of 240 volts is necessary to maintain the 3 kW loading. The element resistance temperature coefficient is 0.0006 per degree centigrade at 20 ⁰C. Calculate the final temperature of the heating element.

A. 345.43 ⁰C

B. 326.42 ⁰C

C. 336.84 ⁰C 

D. 318.48 ⁰C

Question 7:

     A 200-W, 110-V incandescent lamp has a filament having a temperature coefficient of resistance equal to 0.005 at ⁰C. If the normal operating temperature of the bulb is 2500 ⁰C, how much current will the bulb draw at the instant it is turned on. Assume a room temperature of 20 ⁰C.

A. 29.42 A

B. 18.37 A

C. 22.31 A

D. 28.21 A

Question 8:

     The power drawn by a resistive coil made of copper wire is 220 W at 100 V and 20 ⁰C. Calculate the power consume by the  coil at 115 V and 100 ⁰C. The temperature coefficient of resistance at 20 ⁰C is 0.00393.

A. 175 W

B. 211 W

C. 183 W

D. 225 W

Question 9:

     An electric water heater has a rating of 1 kW, 230 V. The coil used as the heating element is 10 m long and has a resistivity of 1.724 x 10^-6 ohm-cm. Determine the required diameter of the wire in mils?

A. 2.43 mils

B. 2.52 mils

C. 3.21 mils

D. 1.35 mils

Question 10:

     When two resistors A and B are connected in series, the total resistance is 36 ohms. When connected in parallel, the total resistance is 8 ohms. What is the ratio of the resistance Ra to resistance Rb . Assume Ra <Rb.

A. 0.5

B. 0.4

C. 0.8

D. 0.6

DC ELECTRIC CIRCUITS - Day 3

Question 1: EE Board March 1998

     Three resistors of 10, 15 and 20 ohms each are connected in parallel. What is the equivalent resistance?

A. 45 ohms

B. 17.2 ohms

C. 0.22 ohm

D. 4.62 ohms

Question 2:

   The equivalent resistance of three resistors A, B and C connected in parallel is 1.714 ohms. If A is twice of B and C is half as much as B, find the equivalent resistance when the three of them are connected in series.

A. 17.5 ohms

B. 21.0 ohms

C. 24.5 ohms

D. 28.0 ohms

Question 3:

     Three resistors of 10, 12 and 15 ohms are connected in parallel. Evaluate the value of current to the parallel system that will make the current in the 10 ohm resistor equal to 2 A.

A. 5 A

B. 6 A

C. 4 A

D. None of these

Question 4:

     Three resistors of 10, 12 and “x” ohms, respectively are connected in parallel across a constant current source of 8 A. Determine “x” if this resistor draws

2.5 A.

A. 10Ω

B. 12Ω

C. 13Ω

D. 11Ω

Question 5:

     Two resistors A and B made of different materials have temperature coefficients of resistance at 20 ⁰C of 0.004 and 0.006 respectively. When connected across a voltage source at 20 ⁰C, they draw current equally. What percentage of the total current at 100 ⁰C does resistor A carry?

A. 47.14%

B. 52.86%

C. 61.34%

D. 38.66%

Question 6:

Two resistor A and B made of different materials have temperature coefficients of resistance of 0.003 and 0.005, respectively. When connected in parallel across a voltage source at 15 ⁰C, it consumes equal power. What is the ratio of the power drawn by resistor B to that in resistor A when temperature rises to 60 ⁰ C? Assume supply voltage is constant.

A. 0.829

B. 0.926

C. 0.964

D. 0.882

Question 7: EE Board March 1998

Three resistor of 10, 15 and 20 ohms each are connected in parallel. What is the total conductance?

A. 0.217 mho

B. 3.41 mhos

C. 4.62 mhos

D. 0.52 mho

Question 8:

     Two heating units x and y are connected across a 100 V supply. Unit y takes twice as much power as unit x. Total power supplied by the source is 2280 watts. Determine the total power drawn by the heating units if they are connected in series across the same source.

A. 615.32 W

B. 506.58 W

C. 582.45 W

D. 604.38 W

Question 9:

     Three resistors R , R  and R  are connected in series-parallel with R1 in series with the parallel combination of R2 and R3. The whole combination is connected across a 120 V DC source. Resistors R1, R2 and R3 take 750 W, 250 W and 200 W, respectively Calculate the resistance R2.

A. 8.10Ω

B. 8.52Ω

C. 7.84Ω

D. 9.22Ω

Question 10:

Two lamps X and Y are connected in series. Lamp X is rated 50 W at 100 V while lamp Y is rated at 100 W at 100 V also. The two lamps are to be connected in series across a 200 V source. What resistance must be connected across lamp A so that each lamp will operate properly?

A. 150 ohms

B. 100 ohms

C. 200 ohms

D. 180 ohms

DC ELECTRIC CIRCUITS - Day 2

Question 1: EE Board October 1997

     A 5-ohm resistance is connected in parallel with a 10-ohm resistance. Another set, a 6-ohm and an 8-ohm resistances are also connected in parallel. The two sets are connected in series. What is the equivalent resistance?

A. 6.76 ohms

B. 9.25 ohms

C. 14.4 ohms

D. 21.2 ohms

Question 2: EE Board March 1998

     Two resistances of 10 and 15 ohms each respectively are connected in parallel. The two are then connected in series with a 5-ohm resistance. What is the equivalent resistance?

A. 11 ohms

B. 12 ohms

C. 10 ohms

D. 9 ohms

Question 3:

     From the circuit as shown, determine the resistance between terminals a &

                                              ___________

                            a     1 Ω      | 2 Ω      3 Ω |     4 Ω        b

–—^^^—–^^^—–^^^—–^^^——–

                                                         |_____________|

A. 1.000 Ω

B. 1.923 Ω

C. 2.083 Ω

D. 2.352 Ω

Question 4: EE Board October 1997

     A 10-ohm and a 20-ohm resistance are connected in parallel. Another resistance of 5-ohm is connected in series with the two. If the supply voltage is 48 volts, what is the current through the 10-ohm resistance?

A. 3.21 A

B. 2.74 A

C. 4.02 A

D. 5.72 A

Question 5:

     A 30-ohm resistor is connected in parallel with a variable resistance R. The parallel combination is then connected in series with a 6-ohm resistor and connected across a 120 V source. Find the minimum value of R if the power taken by R is equal to the power taken by the 6-ohm resistor.

A. 10.35 Ω

B. 12.24 Ω

C. 10.24 Ω

D. 11.46 Ω

Question 6: EE Board March 1998

     Two resistances of 10 and 15 ohms, each respectively are connected in parallel. The two are then connected in series with a 5-ohm resistance. It is then connected across a 12-V battery, what are the current and power?

A. 1.2 A, 17.28 W

B. 0.96 A, 11.52 W

C. 1.09 A, 13.1 W

D. 1.5 A, 20.25 W

Question 7:

     An 8-ohm resistor is connected in series with a parallel combination of two resistors, R and 24 ohms. Determine R if the power consumed by the parllel-connected resistors is equal to the power consumed by the 8-ohm resistor.

A. 10 ohms

B. 16 ohms

C. 12 ohms

D. 20 ohms

Question 8:

     A multi-tap resistor R is connected across a 220-V supply. A voltmeter whose internal resistance is 15-k Ω is connected across the center tap and one end of the supply terminals. If the voltmeter registers 100 V, what is the value of resistor R.

A. 5.5 k Ω

B. 5.0 k Ω

C. 6.0 k Ω

D. 6.5 k Ω

Question 9:

     A potential divider of resistance of 50 ohms is connected across a 100 V DC source. A load resistance of 10 ohms is connected across a tap in the potential divider and the negative terminal of the source. If a current of 4 A flows towards the load, what is the current supplied by the source?

A. 5.32 A

B. 5.05 A

C. 5.21 A

D. 5.48 A

Question 10:

Two resistors A and B are connected in series across a 220 V DC source. When a voltmeter with an internal resistance of 10 k Ω ohms, is connected across resistor A, the instrument reads 100 V and when connected across resistor B, it reads 80 volts. Find the resistance of resistor A.

A. 4 k Ω

B. 3 k Ω

C. 5 k Ω

D. 6 k Ω

DC ELECTRIC CIRCUITS - Day 1

Question 1: EE Board April 1992

     An electric kettle was marked 500 W, 230 V found to take 15 minutes to bring 1 kilogram of water at 15 ⁰C to boiling point. Determine the heat efficiency of the kettle.

A. 79.1%

B. 75.3%

C. 72.4%

D. 74.8%

Question 2: EE Board October 1997

     A process equipment contains 100 gallons of water at 25 ⁰C. It is required to bring it to boiling in 10 minutes. The heat loss is estimated to be 5%. What is the kW rating of the heater?

A. 125 kW

B. 252 kW

C. 50.5 kW

D. 207 kW   

Question 3: EE Board October 1989

     A total of 0.8 kg of water at 20 ⁰C is placed in a 1-kW electric kettle. How long a time in minute is needed to raise the temperature of the water to 100 ⁰C?

A. 4.46 min.

B. 5.32 min

C. 6.34 min

D. 4.56 min

Question 4: EE Board October 1998

     How many calories does an electric heater of 100 watts generate per second?

A. 10

B. 23.88

C. 1000

D. 42.25

Question 5: EE Board October 1997

     The electric energy required to raise the temperature of water in a pool is 1000 kWh. If the heat losses are 25%, the heating energy required will be ___.

A. 1111 kWh

B. 1266 kWh

C. 1750 kWh

D. 1333 kWh

Question 6: EE Board April 1992

     An electric heater carries 12 A at 110 V, is submerged in 22.5 lbs of water for 30 minutes. What will be the final temperature of the water if its initial temperature is 35 ⁰F?

A. 135.43 ⁰F

B. 125.42 ⁰F

C. 133.56 ⁰F

D. 128.33 ⁰F

Question 7: EE Board October 1990

     In an electric heater the inlet temperature is 15 ⁰C. Water is flowing at the rate of 300 grams per minute. The voltmeter measuring voltage across the heating element reads 120 volts and an ammeter measuring current taken reads 10 amperes. When steady state is finally reached, what is the final reading of the outlet thermometer?

A. 57.6 ⁰C

B. 68.4 ⁰C

C. 72.6 ⁰C

D. 42.6 ⁰C

Question 8: EE Board October 1991

     Four cubic meters of water is to be heated by means of four 1.5 kW, 230-V immersion heating elements. Assuming the efficiency of the heater as 90%, determine the time required boiling the water if the initial temperature is 20 ⁰C and if all four elements are connected in parallel.

A. 71 hrs

B. 63 hrs

C. 69 hrs

D. 66 hrs

Question 9: EE Board October 1991

     Four cubic meters of water is to be heated by means of four 1.5 kW, 230-V immersion heating elements. Assuming the efficiency of the heater as 90%, determine the time required boiling the water if the initial temperature is 20 ⁰C and if the elements are connected two in series in parallel with two in series.

A. 275.6 hrs

B. 295.3 hrs

C. 252.2 hrs

D. 264.4 hrs

Question 10: EE Board April 1997

     A circuit consisting of three resistors rated: 10 ohms, 15 ohms and 20 ohms are connected in delta. What would be the resistances of the equivalent wye connected load?

A. 0.30, 0.23 and 0.15 ohm

B. 3.0, 4.0 and 5.0 ohms

C. 3.33, 4.44 and 6.66 ohms

D. 5.77, 8.66 and 11.55 ohms

Question 11: EE Board October 1994

     The equivalent wye element of 3 equal resistors each equal to R and connected in delta is

A. R

B. 3/2R

C. R/3

D. 3R

Question 12:

     Three resistors of 6-ohm resistance are connected in delta. Inside the delta another three 6-ohm resistors are connected in wye. Find its resistance between any two corners.

A. 2 ohms

B. 3 ohms

C. 4 ohms

D. 1 ohm

BASIC PRINCIPLES - Day 3

Question 1:

    A positively charged dielectric has a charge of 2 coulombs. If 12.5 x 10¹⁸ free electrons are added to it, what will be the net charge on the said dielectric?

A. 4 C

B. -2 C

C. 8 C

D. Zero

Question 2:

    A battery can deliver 10 joules of energy to move 5 coulombs of charge. What is the potential difference between the terminals of the battery?

A. 2 V

B. 50 V

C. 0.5 V

D. 5 V

Question 3:

     A cloud of 2.5 x 10¹⁹ electrons move past a given point every 2 seconds. How much is the intensity of the electron flow?

A. 1 A

B. 2 A

C. 2.5 A

D. 1.5 A

Question 4:

     The current in an electric lamp is 5 amperes. What quantity of electricity flows towards the filament in 6 minutes?

A. 30 C

B. 3600 C

C. 72 C

D. 1800 C

Question 5:

     A constant current of 4 A charges a capacitor. How long will it take to accumulate a total charge of 8 coulombs on the plates?

A. 2 s

B. 32 s

C. ½ s

D. 12 s

Question 6: EE Board March 1998

     The substation bus bar is made up of 2-iches round copper bars 20 ft. long. What is the resistance of each bar if resistivity is 1.724 x 10^-6 ohm-cm.

A. 7.21 x 10^-5 ohm

B. 13.8 x 10^-6 ohm

C. 5.185 x 10^-5 ohm

D. 2.96 x 10^-5 ohm

Question 7: EE Board October 1997

     Determine the resistance of a bus bar made of copper if the length is 10 meters long and the cross-section is a 4 x 4 cm². Use 1.7241 micro ohm-cm as the resistivity.

A. 2.121 x 10^-4 ohm

B. 4.312 x 10^-4 ohm

C. 3.431 x 10^-5 ohm

D. 1.078 x 10^-4 ohm

Question 8:

     Nichrome ribbon resistor elements each has a resistance of 1 ohm. The element is made from sheet of nichrome alloy, 0.025 cm thick. If the width of the ribbon is 0.3 cm, what length is required per element? Assume specific resistance of nichrme alloy to be 109 µΩ-cm.

A. 68.8 cm

B. 62.1 cm

C. 70.7 cm

D. 67.4 cm

Question 9: EE Board October 1991

     One turn of a copper bar is produced by cutting a copper washer along a radius and spreading the ends. The washer is cut from soft-drawn copper having a resistivity at 20⁰C of 1.732 x 10^-6 ohm-cm. The washer is 0.125 inch thick and has inside diameter and outside diameter of 1 inch and 9 inches respectively. Calculate the exact resistance between the two ends of the turn to direct current, taking into account the non-uniform current distribution. Assume the contact along the ends of the turn to be perfect over the entire cross-section.

A. 12.74 x 10^-6 ohm

B. 15.53 x 10^-6 ohm

C. 17.22 x 10^-6 ohm

D. 14.83 x 10^-6 ohm

  

Question 10: EE Board October 1990

     Determine the resistance of a conductor 0.10 m long, with a uniform diameter of 1.0 cm and having a resistivity which varies as a function of length L measured from one end of the conductor according to the formula: ρ = 0.003 + 10^-4 L² ohm-cm.

A. 0.0852 ohm

B. 0.0915 ohm

C. 0.0806 ohm

D. 0.0902 ohm

BASIC PRINCIPLES - Day 2

Question 1: EE Board April 1992

     A coil has 6,000 turns of wire and a resistance of 380 ohms. The coil is rewound with the same quantity (weight) of wire, but has 13,400 turns. How many ohms will the new coil have?

A. 1895 ohms

B. 1825 ohms

C. 1792 ohms

D. 1905 ohms

Question 2: EE Board April 1992

     A copper wire of unknown length has a resistance of 0.80 ohm. By successive passes through drawing dies, the length of the wire is increased to 2 ½ times its original value. Assuming that resistivity remains unchanged during the drawing process, determine the new value of its resistance.

A. 4 Ω

B. 3 Ω

C. 5 Ω

D. 6 Ω

Question 3: EE Board October 1998

     A one-meter rod of 2-cm diameter is drawn until its resistance is 100 times the initial resistance. Its length afterward is?

A. 10 m

B. 100 m

C. 12.5 M

D. 5 m

Question 4: EE Board April 1993

     A kilometer of wire having a diameter of 11.7 mm and a resistance of 0.031 ohm is drawn down so that its diameter is 5.0 mm. What does its resistance become?

A. 0.85 ohm

B. 0.78 ohm

C. 0.93 ohm

D. 0.81 ohm

Question 5:

     A conductor whose diameter is 0.175 inch has a resistance of 0.5 ohm. The wire is drawn through a series of dies until its diameter is reduced to 0.08 inch. Assuming the specific resistance of the material remains constant, what is the resistance of lengthened conductor?

A. 11.45 Ω

B. 10.22 Ω

C. 12.75 Ω

D. 10.82 Ω

Question 6: EE Board April 1995

     A certain wire has a resistance R. The resistance of another wire identical with the first except for having twice its diameter is

A. 4R

B. ½R

C. 2R

D. ¼ R

Question 7:

     A given wire has a resistance of 17.5 ohms. If its length is 560 m, how much length must be cut-off from the wire in order to reduce its resistance to 12.5 ohms.

A. 160 m

B. 170 m

C. 145 m

D. 155 m

Question 8: EE Board October 1996

     What is the size in square millimeter (mm²) is the cable of 250 MCM size?

A. 118.656 mm² 

B. 126.675 mm²

C. 112.565 mm²

D. 132.348 mm²

Question 9:

     A 500 MCM ACSR cable has 37 strands. Determine the diameter in mils of each strand.

A. 116.25

B. 120.24

C. 118.34

D. 110.35

Question 10:

     A copper transmission line is to be replaced by one of aluminum having the same total resistance. If the cross sectional area of the copper wire is 500 MCM, what would be the cross sectional area of the new aluminum wire?

A. 800 MCM

B. 820 MCM

C. 850 MCM

D. 900 MCM