*Bob Doyle, Columnist*

**Cumberland Times-News**

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Just as in previous summers, I have been teaching a two semester physics course. Each summer course is taught by daily classes for six weeks (compared to two to three meetings a week for 15 weeks).

With each course, I learn in a few classes how well the students process quantities (such as voltage, current, power) which are often connected by equations (connections that exist between the quantities).

Each day a student gets a worksheet which lists an integer named X and a different integer called Y. (The X and Y values vary from student to student.) The worksheets introduce a chapter and are modeled after the textbook. So if a student reads the text prior to class, it will introduce the quantities dealt in the worksheet.

The top half of the worksheet are my typed remarks using everyday examples to describe the quantities so the students can better relate to them.

This top half of the worksheet also presents the main equations for the quantities. The second half of the worksheet are problems, done both by the instructor (me) and the students, each with a different set of numbers for the quantities.

So on the board, I carefully work the problems using my own X and Y while the students do the same problems with their own X and Y values. The students can either work out their problems on their own (independent) or watch how I treat my numbers and see what must be done for their numbers (imitation).

The value of this strategy is that everyone has a different set of correct answers. I encourage the students to help each other out. Also I encourage students to ask me questions as well.

About half of the questions go to the instructor while the other half of the questions are answered by students. This approach keeps the students involved in the class; the worksheets are turned in at the end of the class, graded and returned to the students at the next class.

The worksheets constitute about 35 percent of a student’s grade. The worksheet’s high weight reduces student absences.

Here’s an abbreviated example of worksheet on electricity: Four key electrical quantities are Voltage (similar to water pressure), Current (similar to water flow), Resistance (similar to the difficulty that water has in going from one place to another) and Power (the same as the rate of work done per unit time).

Just as you need water pressure so your faucets work, you need voltage to cause electricity to flow in an electrical circuit (a pathway for electricity). Just as high water flow requires wide pipes, high currents require thick wires to handle the flow of electricity.

A narrow pipe restricts the flow of water (high resistance) while a wide pipe allows rapid water flow (low resistance). Power for water involves both strong water pressure and high current flow. A thick garden hose allows you to quickly remove any mud stuck to the sides of your car while a hand water pistol would take a lot longer.

Key equations: Voltage = Current x Resistance and Power = Voltage * Current. The two equations are of the form A = B x C. So if you are given A and B, then C = A/B Likewise if you are given A and C, then B = A/C. Units for the four electrical quantities are Volts for V, Amps for C, Ohms for Resistance and Watts for Power.

Suppose you are given X = 4 and Y = 9. 1. If an electrical circuit has a battery of Y volts and a resistance of X ohms, what is the circuit’s current? 2.

For the same X and Y values, if a battery powered night light has a power of Y/X watts and relies on a voltage of Y Volts, solve for its current. (Answers are 1. 0.44 amps 2. 0.25 amps )

SKY SIGHTS AHEAD: The dawn sky features three planets: bright Jupiter in the Southeast, Mars lower and closer to East and Mercury very low in the East. 5:30 a.m. is the best time to spot the three planets from a site with a flat eastern horizon.

Tomorrow, a slender crescent moon will also be seen low in the east about 5:45 a.m. On Tuesday afternoon, the moon will swing from the morning side of the sun to the evening side.

By this coming Friday, a slender crescent moon may be seen low in the west about 8:45 p.m. The brilliant planet Venus will be seen above and slightly to the right of the moon.

On Saturday at dusk, the moon will be wider, brighter and well to the left of Venus.

Bob Doyle invites any readers comments and questions. E-mail him at rdoyle@frostburg.edu . He is available as a speaker on his column topics.