27. Resistors & DC Circuits

A strip of silicon 1.8 cm wide and 1.0 mm thick is immersed in a magnetic field of strength 1.3 T perpendicular to the strip (Fig. 40–53). When a current of 0.28 mA is run through the strip, there is a resulting Hall effect voltage of 18 mV across the strip (Section 27–8). How many electrons per silicon atom are in the conduction band? The density of silicon is 2330 kg/m³.

A lightning bolt hits the ground carrying a current of 3 × 10⁴ A. If the strike lasts 50 ms, how much charge enters the ground?

An aluminum wire consists of the three segments shown in FIGURE P27.64. The current in the top segment is 10 A. For each of these three segments, find the current density J. Place your results in a table for easy viewing.

A superconducting magnet carries a 100 A current through a 0.50-mm-diameter superconducting wire that is wound into a coil. How much charge flows through the wire in 15 minutes?

What diameter should the nichrome wire in FIGURE P27.62 be in order for the electric field strength to be the same in both wires?

The current in a 2.0 mm x 2.0 mm square aluminum wire is 2.5 A. What are (a) the current density and (b) the electron drift speed?

A hollow copper wire with an inner diameter of 1.0 mm and an outer diameter of 2.0 mm carries a current of 10 A. What is the current density in the wire?

A car battery is rated at 90 A h, meaning that it can supply a 90 A current for 1 h before being completely discharged. If you leave your headlights on until the battery is completely dead, how much charge leaves the battery?

The electron beam inside an old television picture tube is 0.40 mm in diameter and carries a current of 50 μA. This electron beam impinges on the inside of the picture tube screen. How many electrons strike the screen each second?

You need to design a 1.0 A fuse that 'blows' if the current exceeds 1.0 A. The fuse material in your stockroom melts at a current density of 500 A/cm². What diameter wire of this material will do the job?

A sculptor has asked you to help electroplate gold onto a brass statue. You know that the charge carriers in the ionic solution are singly charged gold ions, and you've calculated that you must deposit 0.50 g of gold to reach the necessary thickness. How much current do you need, in mA, to plate the statue in 3.0 hours?

The biochemistry that takes place inside cells depends on various elements, such as sodium, potassium, and calcium, that are dissolved in water as ions. These ions enter cells through narrow pores in the cell membrane known as ion channels. Each ion channel, which is formed from a specialized protein molecule, is selective for one type of ion. Measurements with microelectrodes have shown that a 0.30-nm-diameter potassium ion (K⁺) channel carries a current of 1.8 pA. How many potassium ions pass through if the ion channel opens for 1.0 ms?