Exam 21: Electric Charge and Electric Field

Resistivity: Nichrome wire, often used for heating elements, has resistivity of 1.0 × 10^-6 Ω ∙ m at room temperature. What length of wire of diameter 0.250 mm is needed to wind a resistor that has 50 ohms at room temperature?

Power: The voltage and power ratings of a particular light bulb, which are its normal operating values, are 110 V and 60 W. Assume the resistance of the filament of the bulb is constant and is independent of operating conditions. If the light bulb is operated with a current that is 50% of the current rating of the bulb, what is the actual power drawn by the bulb?

Resistivity and temperature: A piece of wire 58.4 cm long carries a current I when a voltage V is applied across its ends at a temperature of 0°C. If the resistivity of the material of which the wire is made varies with temperature as shown in the graph in the figure, what length of the same diameter wire is needed so that the same current flows when the same voltage is applied at temperature 400°C?

Basics of ac circuits: A 500-W device is connected to a 230-V ac power source. What is the peak voltage across this device?

Resistivity: What length of a certain metal wire of diameter 0.15 mm is needed for the wire to have a resistance of 15 Ω? The resistivity of this metal is 1.68 × 10^-8 Ω ∙ m.

Resistivity: A 2.0 mm diameter wire of length 20 m has a resistance of 0.25 Ω. What is the resistivity of the wire?

Resistivity and temperature: A platinum wire is used to determine the melting point of indium. The resistance of the platinum wire is 2.000 Ω at 20°C and increases to 3.072 Ω as the indium starts to melt. What is the melting point of indium? The temperature coefficient of resistivity for platinum is 3.9 × 10^-3(C°)^-1.

Drift velocity: A wire has a cross-sectional area of 0.10 mm². If there are 4.0 × 10²⁸ atoms per cubic meter in this wire, and if each atom contributes 2 free electrons, what is the drift velocity of the electrons when the current in the wire is 6.0 A? (e = 1.60 × 10^-19C)

Current density: If the current density in a wire or radius R is given by J = kr, 0 < r < R, what is the current in the wire?

Power: A 400-W computer (including the monitor) is turned on for 8.0 hours per day. If electricity costs 10¢ per kWh, how much does it cost to run the computer annually for a typical 365-day year?

Ohm's law: When a voltage difference is applied to a piece of metal wire, a current flows through it. If this metal wire is now replaced with a silver wire having twice the diameter of the original wire, how much current will flow through the silver wire? The lengths of both wires are the same, and the voltage difference remains unchanged. (The resistivity of the original metal is 1.68 × 10^-8 Ω ∙ m, and the resistivity of silver is 1.59 × 10^-8 Ω ∙ m.)

Current: In an electroplating process, copper (ionic charge +2e, atomic weight 63.6 g/mol) is deposited using a current of 10.0 A. What mass of copper is deposited in 10.0 minutes? Avogadro's number is 6.022 × 10²³ molecules/mol and e = 1.60 × 10^-19 C.

Electric field in a wire: A silver wire with resistivity carries a current density of What is the magnitude of the electric field inside the wire?

Electric field in a wire: The resistivity of gold is at room temperature. A gold wire that is 0.9 mm in diameter and 14 cm long carries a current of 940 mA. What is the electric field in the wire?