The resultant resistance of two resistance wires in series is 108 ohms, and in parallel, it is 24 ohms. Find the value of the individual resistances.
Answer (2)
Call the two resistors 'x' and 'y'.
In series, the resultant resistance is their sum: x + y = 108 Notice that y = 108 - x. I think we'll use that very soon.
In parallel, the resultant resistance is (their product) / (their sum) = xy/108 = 24
Multiply each side by 108:
xy = 2,592
Substitute for 'y' :
x(108 - x) = 2,592
108x - x² = 2,592
-x² + 108x - 2,592 = 0
x² - 108x + 2,592 = 0
Use the quadratic formula to find:
x = 72 . . . then y = 108 - 72 = 36 or x = 36 . . . then y = 108 - 36 = 72
The individual resistors are 36Ω and 72Ω .
The two resistances are 36 ohms and 72 ohms. This is found by using equations for resistances in series and parallel, along with the quadratic formula. The process involves substituting and rearranging equations to isolate the variables.
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