Basic Principles

Problem 21: The resistance of a copper wire at \(30^\circ C\) is 50 ohms. If the temperature coefficient of copper at \(0^\circ C\) is 0.00427, what is the resistance at \(100^\circ C\)?

Problem 22: The shunt field winding of a shunt generator has a resistance of 80 ohms at \(20^\circ C\). After several hours of continuous operation, the winding temperature rises to \(50^\circ C\). How much is the winding resistance under this condition. Assume the resistance temperature coefficient of copper to be 0.004 ohm per degree at \(0^\circ C\).

Problem 23: The field windings of a series motor has a resistance of 120 ohms at \(15^\circ C\). After running for two hours, the resistance increases to 140 ohms. If the temperature coefficient of the windings at \(0^\circ C\) is 0.004, find the new temperature of the windings.

Problem 24: The resistance of a wire is 126.48 ohms at \(100^\circ C\) and 100 ohms at \(30^\circ C\). Determine the temperature coefficient of copper at \(0^\circ C\).

Problem 25: Two wires A & B made from two different materials have temperature coefficient of resistance equal to 0.0025 and 0.0005 ohm per \(^\circ C\), respectively. It is desired to make a coil of wire having a resistance of 1200 ohms with a temperature coefficient of 0.001, using suitable lengths of the two given wires connected in series. Determine the required resistance of wire A.

Problem 26: Two heating elements which is 500 ohms and 250 ohms are connected in series with temperature coefficients of 0.001 and 0.003 ohms per \(^\circ C\), respectively at \(20^\circ C\). Calculate the effective temperature coefficient of the combination.

Problem 27: A cylindrical rubber insulated cable has a diameter of 0.18 inch and an insulation thickness of 0.25 inch. If the specific resistance of rubber is \(10^{14}\) ohm-cm, determine the insulation resistance per 1000-ft length of the cable.

Problem 28: The diameter of a given bare conductor is 0.50 inch. A thermoplastic insulation with thickness of 0.1 inch is wrapped around to insulate the conductor. Determine the insulation resistance of this conductor per meter. Assume specific resistance of thermoplastic insulation to be \(2 \times 10^{14}\) ohm-cm.

Problem 29: The insulation resistance of a kilometer of the cable having a diameter of 2 cm and an insulation thickness of 2 cm is 600 ohms. If the thickness of the insulation is increased to 3 cm, find the insulation resistance of the cable.

Problem 30: The resistance of 120 meters of wire is 12 ohms. What is its conductance?