SOLUTION: Two questions; (1) A resistor has a resistance of 30 ohms. What size resistor should be put with it, in parallel, to obtain a resistance of 3 ohms? (the answer is 10/3 ohms just

Question 1172077: Two questions;
(1) A resistor has a resistance of 30 ohms. What size resistor should be put with it, in parallel, to obtain a resistance of 3 ohms? (the answer is 10/3 ohms just need the work)
(2) The harmonic mean of two numbers, a and b, is a number M, such that the reciprocal of M is the average of the reciprocal of a and b. Find a formula for the harmonic mean.
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
.


(1)  Let x be the unknown resistance.


     Then the effective resistance R satisfies this equation

         =  + .


     It gives you an equation to find x

         =  + ,


     which implies

         =  - ,   or

         =  -  =  = .


     Hence,  x =  ohms = 3.333 ohms.      ANSWER



(2)  The direct and literal translation of words into Math is this formula


          = .


     From this formula,


          M =  = .    ANSWER

Solved and explained.

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