Basic Principles

Problem 1: A positively charged dielectric has a charge of 2 coulombs. If \(12.5 \times 10^{18}\) free electrons are added to it, what will be the net charge on the said dielectric?

Problem 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?

Problem 3: A cloud of \(2.5 \times 10^{19}\) electrons move past a given point every 2 seconds. How much is the intensity of the electron flow?

Problem 4: The current in an electric lamp is 5 amperes. What quantity of electricity flows towards the filament in 6 minutes?

Problem 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?

Problem 6: The substation bus bar is made up of 2-inches round copper bars 20 ft. long. What is the resistance of each bar if resistivity is \(1.724 \times 10^{-6}\) ohm-cm.

Problem 7: Determine the resistance of a bus bar made of copper if the length is 10 meters long and the cross-section is a \(4 \times 4 \text{ cm}^2\). Use 1.7241 micro ohm-cm as the resistivity.

Problem 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 nichrome alloy to be 109 micro ohm-cm.

Problem 9: 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 \(20^\circ C\) of \(1.732 \times 10^{-6}\) 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.

Problem 10: 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: \(\rho = 0.003 + 10^{-4} L^2\) ohm-cm.

Problem 11: 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?

Problem 12: 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 \(2\tfrac{1}{2}\) times its original value. Assuming that resistivity remains unchanged during the drawing process, determine the new value of its resistance.

Problem 13: A one-meter rod of 2-cm diameter is drawn until its resistance is 100 times the initial resistance. Its length afterward is?

Problem 14: 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?

Problem 15: 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 the lengthened conductor?

Problem 16: A certain wire has a resistance R. The resistance of another wire identical with the first except for having twice its diameter is:

Problem 17: 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.

Problem 18: What is the size in square millimeter \((\text{mm}^2)\) is the cable of 250 MCM size?

Problem 19: A 500 MCM ACSR cable has 37 strands. Determine the diameter in mils of each strand.

Problem 20: 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?