27. Resistors & DC Circuits

You've decided to protect your house by placing a 5.0-m-tall iron lightning rod next to the house. The top is sharpened to a point and the bottom is in good contact with the ground. From your research, you've learned that lightning bolts can carry up to 50 kA of current and last up to 50 μs. How much charge is delivered by a lightning bolt with these parameters?

Lightning occurs when there is a flow of electric charge (principally electrons) between the ground and a thundercloud. The maximum rate of charge flow in a lightning bolt is about $20,000$ C/s; this lasts for $100$ ms or less. How much charge flows between the ground and the cloud in this time? How many electrons flow during this time?

A linear accelerator uses alternating electric fields to accelerate electrons to close to the speed of light. A small number of the electrons collide with a target, but a large majority pass through the target and impact a beam dump at the end of the accelerator. In one experiment the beam dump measured charge accumulating at a rate of −2.0 nC/s. How many electrons traveled down the accelerator during the 2.0 h run?

(I) A current of 1.75 A flows in a wire. How many electrons are flowing past any point in the wire per second?

(II) What is the current in amperes if 1200 Na⁺ ions flow across a cell membrane in 2.8 μs? The charge on the sodium is the same as on an electron, but positive.

The LHC accelerator at CERN (Switzerland) is designed to carry a 0.58-A beam of protons ( q = 1.6 x 10^-19 C ) traveling at very nearly the speed of light ( 3.0 x 10⁸ m/s) around a ring 27 km in circumference. How many protons are in the beam?

For the wire in Fig. 25–38, whose diameter varies uniformly from a to b as shown, suppose a current I = 2.5 A enters at a. If a = 2.5 mm and b = 4.0 mm, what is the current density (assume uniform) at each end?

A 4.5-V battery is connected to a bulb whose resistance is 2.3 Ω. How many electrons leave the battery per minute?

An ammeter has a sensitivity of 35, 000Ω /V. What current in the galvanometer produces full-scale deflection?