A spool of aluminum wire 200 m long and with a diameter of 0.360 mm is at 20.0°C. For aluminum, the resistivity is 2.82 x 10-80 m and the temperature coefficient of resistivity is 3.90 x 10-3 (°C)-¹. (a) What is the magnitude of the electric field (in V/m) in the wire if it carries a current of 0.400 A? V/m (b) What is the electric power (in W) delivered to the spool while it carries a current of 0.400 A? W (c) What is the power (in W) delivered to the spool if the potential difference across the wire is held constant and the temperature is increased to 310°C? W

When a straight wire is heated, its resistance changes according to the equation R = R0 [1 + (T T0)] (Eq. 17.7), where is the temperature coefficient of resistivity. (a) Show that a more precise result, which includes the length and area of a wire change when it is heated, is R=R0[1+(TT0)][1+(TT0)][1+2(TT0)] where is the coefficient of linear expansion. (See Topic 10.) (b) Compare the two results for a 2.00-m-long copper wire of radius 0.100 mm, starting at 20.0C and heated to 100.0C.

A close analogy exists between the flow of energy by heat because of a temperature difference (see Section 19.6) and the flow of electric charge because of a potential difference. In a metal, energy dQ and electrical charge dq are both transported by free electrons. Consequently, a good electrical conductor is usually a good thermal conductor as well. Consider a thin conducting slab of thickness dx, area A, and electrical conductivity , with a potential difference dV between opposite faces. (a) Show that the current I = dq/dt is given by the equation on the left: ChargeconductionThermalconductiondqdt=A|dVdx|dQdt=kA|dTdx| In the analogous thermal conduction equation on the right (Eq. 19.17), the rate dQ/dt of energy flow by heat (in SI units of joules per second) is due to a temperature gradient dT/dx in a material of thermal conductivity k. (b) State analogous rules relating the direction of the electric current to the change in potential and relating the direction of energy flow to the change in temperature.

Review. When a straight wire is warmed, its resistance is given by R = R0,[1 + a(T T0)] according to Equation 27.20, where a is the temperature coefficient of resistivity. This expression needs to be modified if we include the change in dimensions of the wire due to thermal expansion. For a copper wire of radius 0.100 0 mm and length 2.000 m, find its resistance at 100.0C, including the effects of both thermal expansion and temperature variation of resistivity. Assume the coefficients are known to four significant figures.

A particle accelerator produces a beam with a radius of 1.25 mm with a current of 2.00 mA. Each proton has a kinetic energy of 10.00 MeV. (a) What is the velocity of the protons? (b) What is the number (n) of protons per unit volume? (b) How many electrons pass a cross sectional area each second?

Integrated Concepts (a) What energy is dissipated by a lightning bolt having a 20,000-A current, a voltage of 1.00102 MV, and a length of 1.00 ms? (b) What mass of tree sap could be raised from 18.0°C to its boiling point and then evaporated by this energy, assuming sap has the same thermal characteristics as water?

A 0.900-V potential difference is maintained across a 1.50-m length of tungsten wire that has a cross-sectional area of 0.600 mm2. What is the current in the wire?

Question A spool of copper wire 200 m long and with a diameter of 0.320 mm is at 20.0°C. For copper, the resistivity is 1.70 X 10-8 Q·m and the temperature coefficient of resistivity is 3.90 X 10-3 (°C)~1. (a) What is the magnitude of the electric field (in V/m) in the wire if it carries a current of 0.400 A? V/m (b) What is the electric power (in W) delivered to the spool while it carries a current of 0.400 A? W (c) What is the power (in W) delivered to the spool if the potential difference across the wire is held constant and the temperature is increased to 280°C? W

p2

Current and Resistance Problem 18:   Consider two wires made of different materials. Wire A has a conductivity of 1.9 × 107 Ω-1m-1, and wire B has a conductivity of 8.5 × 107 Ω-1m-1. Part (a)  Wire A has a circular cross-section with radius 2.74 mm. If there is an electric field of 0.059 V/m inside it, how much current, in amperes, is flowing through it?  Part (b)  Wire B has a square 2.74 mm × 2.74 mm cross-section. If wire B has the same electric field as Wire A did in part (a), what current, in amperes, would be passing through it?