The resultant resistance of two resistance wires in series combination is 108 ohms and in parallel combination 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 individual resistances of the two wires are 72 ohms and 36 ohms. These values can be derived from the equations for resistances in series and parallel combinations. The calculations confirm these results by solving the equations step-by-step.
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