Basic Electricity Worksheet

Electricity is fast: the effects of electron motion travel at approximately the speed of light (186,000 miles per second). Actual average electron velocity, on the other hand, is very, very slow. A convenient analogy I’ve used to illustrate how electrons may move slowly yet have rapid effect is that of a closed-loop hydraulic system. When the valve is opened, fluid motion throughout the system is immediate (actually, the motion progresses at the speed of sound through the fluid - very fast!), yet the actual velocity of fluid motion is much slower.

Incidentally, the double-chevron symbols indicate an electrical connector pair (plug and jack; male and female).

Despite the rapid progression of the effects of electron motion throughout a circuit (i.e. approximately the speed of light), the actual electron velocity is extremely slow by comparison.

Base figures used in this calculation are as follows:

• Number of free electrons per cubic meter of metal (an example taken from Encyclopedia Brittanica 15th edition, 1983, volume 6, page 551) = 10²⁹ electrons per m³. The metal type was not specified.

• 22 gauge wire has a diameter of 0.025 inches.

Questions like this may be challenging to students without a strong math or science background. One problem-solving strategy I have found very useful is to simplify the terms of a problem until a solution becomes obvious, then use that simplified example to establish a pattern (equation) for obtaining a solution given any initial parameters. For instance, what would be the average electron velocity if the current were 28.96 ×10²¹ electrons per second, the same figure as the number of free electrons residing in the wire? Obviously, the flow velocity would be one wire length per second, or 3 feet per second. Now, alter the current rate so that it is something closer to the one given in the problem (6.25 ×10¹⁸), but yet still simple enough to calculate mentally. Say, half the first rate: 14.48 ×10²¹ electrons per second. Obviously, with a flow rate half as much, the velocity will be half as well: 1.5 feet per second instead of 3 feet per second. A few iterations of this technique should reveal a pattern for solution:

Where,

v = Average electron velocity (feet per second)

I = Electric current (electrons per second)

Q = Number of electrons contained in wire

It is also very helpful to have knowledgeable students demonstrate their solution techniques in front of the class so that others may learn novel methods of problem-solving.

Ask the students about the relative conductivities of metal chassis versus dirt (earth ground). Is a current pathway formed by two metal chassis grounds equivalent to a current pathway formed by two earth grounds? Why or why not? What conditions may affect these relative conductivities?