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Five to One (Posted on 2013-09-27) Difficulty: 3 of 5
A 1 volt battery and five 1 ohm resistors are to be hooked up in a circuit to have 1 ampere of current. How can this be arranged? You must use all five resistors in the circuit.

See The Solution Submitted by Brian Smith    
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Solution Mister resistor Comment 1 of 1

Well, one way would be to short circuit 4 of the resistors and just have one resistor that is not short circuited, but I don't think that is what is in mind.
Note that 2 resistors in parallel have half the resistance of a resistor by itself.
In parallel, resistors add like this:  1/(1/R1 + 1/R2).
In series:  R1 + R2.

If we had just 4 resistors, put 1 and 2 in series as Group 1.
Then put 3 and 4 in series as Group 2.
Finally put Group 1 in parallel with Group 2.

So I thought of a "Wheatstone Bridge - like" arrangement:

                         ____r1____r2___
                       /            |            \
                     /              |              \
      A --------               r5                ------- B
                     \               |              /
                       \             |             / 
                         \__r3___|___r4___/

The 5th resistor, R5 should have no current across it


  Posted by Larry on 2013-09-27 20:30:24
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