Exam 24: Current, Resistance, and Electromotive Force

The heater element of a particular 120-V toaster is a 8.9-m length of nichrome wire, whose diameter is 0.86 mm. The resistivity of nichrome at the operating temperature of the toaster is 1.3 × 10^-6 Ω ∙ m. If the toaster is operated at a voltage of 120 V, how much power does it draw?

If a current of 2.4 A is flowing in a cylindrical wire of diameter 2.0 mm, what is the average current density in this wire?

A cylindrical wire of radius 2.0 mm carries a current of 2.5 A. The potential difference between points on the wire that are 46 m apart is 3.7 V. (a) What is the electric field in the wire? (b) What is the resistivity of the material of which the wire is made?

Two cables of the same length are made of the same material, except that one cable has twice the diameter of the other cable. When the same potential difference is maintained across both cables, which of the following statements are true? (There may be more than one correct choice.)

A 110-V hair dryer is rated at 1200 W. What current will it draw when operating from a 110-V electrical outlet?

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.

A narrow copper wire of length L and radius b is attached to a wide copper wire of length L and radius 2b, forming one long wire of length 2L. This long wire is attached to a battery, and a current is flowing through it. If the electric field in the narrow wire is E, the electric field in the wide wire is

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

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^-19 C)

A proton beam that carries a total current of 1.3 mA has 10.0 mm diameter. The current density in the proton beam increases linearly with distance from the center. This is expressed mathematically as J(r) = J0 (r/R), where R is the radius of the beam and J0 is the current density at the edge. Determine the value of J0.

What must be the diameter of a cylindrical 120-m long metal wire if its resistance is to be 6.0 Ω? The resistivity of this metal is 1.68 × 10^-8 Ω ∙ m.

How much current will be flowing through a 40.0 m length of cylindrical metal wire with radius 0.0 mm if it is connected to a source supplying 16.0 V? The resistivity of this metal is 1)68 × 10^-8 Ω ∙ m.

A silver wire with resistivity 1.59 × 10^-8 Ω ∙ m carries a current density of 4.0 A/mm². What is the magnitude of the electric field inside the wire?

The current in a wire varies with time according to the equation I(t) = 6.00 A + (4.80 A/s)t, where t is in seconds. How many coulombs of charge pass a cross section of the wire in the time period between t = 0.00 s and t = 3.00 s?

A wire of resistivity ρ must be replaced in a circuit by a wire of the same material but 4 times as long. If, however, the resistance of the new wire is to be the same as the resistance of the original wire, the diameter of the new wire must be

The emf and the internal resistance of a battery are as shown in the figure. If a current of 8.3 A is drawn from the battery when a resistor R is connected across the terminals ab of the battery, what is the power dissipated by the resistor R?

The temperature coefficient of resistivity for copper is 0.0068 (C°)^-1. If a copper wire has a resistance of 104 Ω at 20°C, what is its resistance 80°C?

A silver wire has a cross sectional area A = 2.0 mm². A total of 9.4 × 10¹⁸ electrons pass through the wire in 3.0 s. The conduction electron density in silver is 5.8 × 10²⁸ electrons/m3 and e = 1.60 × 10^-19 C. What is the drift velocity of these electrons?

When a voltage difference is applied to a piece of metal wire, a 5.0-mA 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.)

A 1500-W heater is connected to a 120-V line. How much heat energy does it produce in 2.0 hours?