When two resistance connected in and parallel their equivalent resistance are 15 ohm and 56/15 respectively.Find the individual resistance.
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Assuming that only two resistors are involved, the solution to this problem requires solving two simultaneous equations in two unknowns (R1 and R2).
For the series combination: R1 + R2 = 10 [1]
For the parallel combination: (R1•R2) / (R1+R2) = 12/5 [2]
Solve [1] for R1: R1 = 10 - R2 [3]
Substitute [3] into [2]: (10 - R2) ·R2/[(10- R2) + R2] = 12/5
Simplifying: (10·R2 = R2 ^2)/10 = 12/5, or 10·R2 - R2^2 = 24
Meaning R2^2 - 10 R2 + 24 = 0 , or (R2 - 6)•(R2 - 4) = 0
which has two solutions: (a) R2 = 2 or (b) R2 = 4.
If (a) R2 = 6Ω, then R1 = 10 - R2 = 10 - 6 = 4Ω
Alternately, if (b) R2 = 4Ω, then R1 = 10 - R2 = 10 - 4 = 6Ω....
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