SOLUTION: In a parallel circuit, the joint resistance is 8 ohms. If one resistor is 12 ohms less than the second resistor, find both resistors.

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Question 39434: In a parallel circuit, the joint resistance is 8 ohms. If one resistor is 12 ohms less than the second resistor, find both resistors.
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
parallel circuit with resistors A and B, then the total resistance is given by R where

+1%2FR+=+1%2FA+%2B+1%2FB+
+1%2FR+=+B%2F%28AB%29+%2B+A%2F%28AB%29+
+1%2FR+=+%28A%2BB%29%2F%28AB%29+
+R+=+%28AB%29%2F%28A%2BB%29+

so, given our info of one resistor being x and the other being (x-12), we get:

+8+=+%28x%28x-12%29%29%2F%28x%2B%28x-12%29%29+
+8+=+%28x%5E2-12x%29%2F%282x-12%29+
+8%282x-12%29+=+x%5E2-12x+
+16x-96+=+x%5E2-12x+
+0+=+x%5E2-28x%2B96+
+x%5E2-28x%2B96+=+0+
(x-4)(x-24) = 0
so x-4=0 or x-24=0
x=4 or x=24

Now x is not 4 for our resistor problem, since the other resistor would then be 4-12 --> -8. This is physically impossible.

So, the only answer we have is that the resistors are 24 and (24-12) --> 12.

jon.