Supplementary Problems Electrical Circuits

SUPPLEMENTARY PROBLEMS 1. A coil is connected to a constant DC supply of 100V. At start, when it was at the room temperature of 25 ᵒC, it drew a current of 13A. After sometime was 70 ᵒC and the current reduced to 8.5A. Find the current it will draw when its temperature increases further 80 ᵒC. Also, find temperature coefficient of the resistance of the coil material at 25 ᵒC. 2. A circuit consists of four 100W lamps connected in parallel across a 230V supply. In advertently, a voltmeter has been connected in series with the lamps. The resistance of the voltmeter is 1500 ohms and that of the lamps under stated conditions stated six times their value when burning normally. What will be the reading of the voltmeter? 3. A piece of silver wire has a resistance of 1 ohm. What will be the resistance of manganin wire of one – third the length and one – third the diameter, if the specific resistance of manganin is 30 times that of silver? 4. 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 50 X 10 -8 ohm – cm. If the wire is drawn out to three times its original length, by how many times would you expect its resistance to be increased? 5. A tungsten filament lamp has a temperature of 2050 ᵒC and a resistance of 500 ohms when taking normal working current. Calculate the resistance of the when it has a temperature of 25ᵒC. Temperature coefficient of resistance wire (is 0.00029/ᵒC) at 0ᵒC is 0.005/ᵒC. 6. A piece of resistance wire, 15.6 m long and a cross – sectional area 12mm2 at temperature of 0ᵒC, passes a current of 7.9A when connected to a DC supply at 240V. Calculate (a) resistivity of the wire; (b) the current which flow when the temperature rises to 55 ᵒC. The temperature coefficient of resistance of the wire is 0.00029/ᵒC. 7. Calculate the resistance of 1 km long cable, compassed of 19 strands of similar copper conductors, each strand being 1.32 mm in diameter. Allow 5% increased in length for the lay (twist) of each strand in completed cable. Resistivity of copper maybe taken as 1.72 X 10-8 Ω – m. 8. The resistivity of commercial quality of copper is 0.686 μΩ – in at 20 ᵒC. Determine the cross – section in square – in., circular mil, and square mil of 121 lbs of this copper when the length is 600 ft. The weight per cubic inch of copper is 0.321 lbs. 9. The nichrome unit (ρ = 660) is a toaster has an R of 24 ohms. What is the R of a copper conductor of equal cross – sectional area, but 10 times as long as the nichrome unit? 10. A coil of copper wire has a length of 600 ft. what is the length of an aluminum conductor if its cross – sectional area and resistance are the same as those of the copper coil? 11. A kilometer of wire having a diameter of 11.22 mm and a resistance of 0.031 ohm is drawn so that its diameter is 5mm. What does it resistance become? 12. Three resistors of 6-ohm resistance are connected in delta. Inside the delta another 6-ohm resistors are connected in wye. Find its resistance between any two corners. 13. 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. 14. 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 parallel connected resistors is equal to the power consumed by the 8 ohm resistor. 15. For Figure (a) shown below, solve for the value of I 1 and I2.

30 (a) 16. 17. 18. 19.

(b)

For Figure (b), solve for the Value of R. For the Figure shown in Figure (c), solve for the value of the current I and RAB. Solve for the resistance between terminals A and B shown in Figure (d) Solve for the resistance between terminals A and B shown in Figure (e)

5 10

10

I 10

A 18

B

36

6

(c)

(d)

A

B

all resistances = 1 ohm (e)