Question 232822: three resistors with values of 1000 ohms, 2200 ohms and 3900 ohms are wired in parallel.To find the total resistance one must add the reciprocals.In the book I am studying the formula to solve is given as:
1/R = 1/R1 + 1/R2 + 1/R3 = 1/1K + 1/2.2K + 1/3.9K = 1/584.5, therefore R = 584.5 ohms
Can you show me how this answer is computed in long hand?
Thanks,
David
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! three resistors with values of 1000 ohms, 2200 ohms and 3900 ohms are wired in parallel.To find the total resistance one must add the reciprocals.In the book I am studying the formula to solve is given as:
1/R = 1/R1 + 1/R2 + 1/R3 = 1/1K + 1/2.2K + 1/3.9K = 1/584.5, therefore R = 584.5 ohms
Can you show me how this answer is computed in long hand?
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It's as you did it. You can do 2 resistors 1st, then add the 3rd as a check.
There's a shortcut that works easily with 2 resistors, sum/product
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The 1K and 2.2K --> 1*2.2/(1+2.2)
= 2.2/3.2 = 11/16 K
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Then:
(11/16)*3.9/(11/16 + 3.9) = 2.68125/4.5875
= 0.58446... K
= 584 ohms
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