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Two resistors in parallel are equivalent to 6 ohm and in series the equivalent...

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mikerhyme | Student, Kindergarten | (Level 1) Salutatorian

Posted September 12, 2013 at 5:07 PM via web

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Two resistors in parallel are equivalent to 6 ohm and in series the equivalent resistance is 16 ohm. Can the resistance of the resistors be determined.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 12, 2013 at 5:16 PM (Answer #1)

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The equivalent resistance of two resistors R1 and R2 in series is R = R1 + R2. If the resistors are connected in parallel, the equivalent resistance R is related by `1/R = 1/(R1) + 1/(R2)`

Let the resistance of the two resistors that has to be determined be A and B.

`A + B = 16` and `1/6 = 1/A + 1/B`

`1/6 = 1/A + 1/B`

=> `1/6 = (A + B)/(A*B)`

Substitute `A = 16 - B`

=> `1/6 = (16 - B + B)/((16 - B)*B)`

=> `1/6 = 16/((16 - B)*B)`

=> `16B - B^2 = 96`

=> `B^2 - 16B + 96 = 0`

This equation only has complex solutions for B.

There are no two resistors which when connected in series give an equivalent resistance of 16 ohm and when connected in parallel give an equivalent resistance of 6 ohm.

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