A ductile metal wire has resistance R. What will be the resistance of this wire in terms of R if it is stretched to three times its original length, assuming that the density and resistivity of the material do not change when the wire is stretched? (Hint: The amount of metal does not change, so stretching out the wire will affect its cross-sectional area.)

A copper transmission cable 100 km long and 10.0 cm in diameter carries a current of 125 A. (b) How much electrical energy is dissipated as thermal energy every hour?

(b) What is the resistance of a carbon rod at 25.8°C if its resistance is 0.0160 Ω at 0.0°C?

A hollow aluminum cylinder is 2.50 m long and has an inner radius of 2.75 cm and an outer radius of 4.60 cm. Treat each surface (inner, outer, and the two end faces) as an equipotential surface. At room temperature, what will an ohmmeter read if it is connected between (a) the opposite faces and (b) the inner and outer surfaces?

In household wiring, copper wire 2.05 mm in diameter is often used. Find the resistance of a 24.0-m length of this wire.

A cylindrical tungsten filament 15.0 cm long with a diameter of 1.00 mm is to be used in a machine for which the temperature will range from room temperature (20°C) up to 120°C. It will carry a current of 12.5 A at all temperatures. (c) What will be the maximum potential drop over the full length of the filament?

A 2.0-mm-diameter wire formed from a composite material has a resistivity that decreases with distance along the wire as ρ=ρ₀e^−αˣ, where ρ₀=4.0×10^−5 Ω m , x (in m) is measured from one end of the wire, and the constant α=4.0 m^−1. What is the resistance of a 50-cm-long length of this wire?

A hollow copper sphere has inner radius 1.0 cm and outer radius 2.5 cm. A 5.0 A current flows radially outward from the inner surface to the outer surface. What is the electric field strength at r=2.0 cm?

A 12 V car battery dies not so much because its voltage drops but because chemical reactions increase its internal resistance. A good battery connected with jumper cables can both start the engine and recharge the dead battery. Consider the automotive circuit of FIGURE P28.64.b. How much current is the dead battery alone able to drive through the starter motor?