E&M Worksheet 3.1

A wire of resistance R dissipates power P when a current I passes through it. The wire is replaced by another wire with resistance 3R. The power dissipated by the new wire when the same current passes through it is

• P/9

• P/3

• P

• 3P

• 6P

The power dissipated in a wire carrying a constant electric current I may be written as a function of I, the length L of the wire, the diameter d of the wire, and the resistivity ρ of the material in the wire. In this expression, the power dissipated is directly proportional to which of the following?

• L only

• d only

• L and ρ only

• d and ρ only

• L, d, and ρ

A metal wire has a resistance R when it is at a temperature T. The wire is melted and all of the metal is used to reform it into a new wire 4 times as long. What is the resistance of the new wire at temperature T?

• R

• 2R

• 4R

• 8R

• 16R

A narrow beam of protons produces a current of 1.6 x 10^‑3 A. There are 10⁹ protons in each meter along the beam. Of the following, which is the best estimate of the average speed of the protons in the beam?

• 10^‑15 m/s

• 10^‑12 m/s

• 10^‑7 m/s

• 10⁷ m/s

• 10¹² m/s

Two conducting spheres, X and Y. have the same positive charge +Q, but different radii (r_x > r_y) as shown above. The spheres are separated so that the distance between them is large compared with either radius.  If a wire is connected between them, in which direction will current be directed in the wire?

• From X to Y

• From Y to X

• There will be no current in the wire

• It cannot be determined without knowing the magnitude of Q

• It cannot be determined without knowing whether the spheres are solid or hollow

When lighted, a 100‑watt light bulb operating on a 110‑volt household circuit has a resistance closest to

• 10^‑2 Ω

• 10^‑1 Ω

• 1 Ω

• 10 Ω

• 100 Ω

A 12‑volt storage battery, with an internal resistance of 2 Ω, is being charged by a current of 2 amperes as shown in the diagram above. Under these circumstances, a voltmeter connected across the terminals of the battery will read

• 4 V

• 8 V

• 10 V

• 12 V

• 16 V

The emf of a battery is 12 volts. When the battery delivers a current of 0.5 ampere to a load, the potential difference between the terminals of the battery is 10 volts. The internal resistance of the battery is

• 1 Ω

• 2 Ω

• 4 Ω

• 20 Ω

• 24 Ω