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the resultant resistance of two resistance wires in series combination is 108 ohm and in parallel combination is 24 ohm. find the value of individual resistance

Sagot :

AL2006
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 .

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