PhysicsLAB Amusing Problems
The Cycle Shop

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In this shocking episode, Dr. J and his crew invest in a new part-time business. With the high price of gasoline, many of the rental car companies have started renting motorcycles. Of course the leader in this field is Hertz (after all, a cycle per second is a fantastic rate of business). On the other hand, Avis and some of the other companies have shown a resistance to this current trend because of their concern over the potential business. Dr. J decides to go one step further and rent electric motorcycles. It seems like a natural: J. Jr. will handle the renting; Timex will serve as the mechanic (his specialty is timing engines); and even Tripod can show first-time customers how to keep their balance. Dr. J designs these electric motorcycles himself. The only drawback to them is the speed. Whereas a gas-guzzling Harley can reach 70 MPH and over, Dr. J's model can only reach 7 MPH (he names it a Hardly). A problem arises while assembling the first of these cycles. There are three 10-ohm resistors left, but the circuit diagram showing the proper way to wire them is blurred. After thinking a bit, Timex says, "How many ways can you do this, anyway?" Dr. J says that there are seven different combinations. (Not every combination need use all three resistors.)
Find the total resistance for each of these seven combinations.

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