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

Algebra ->  Rational-functions -> 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      Log On


   

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) About Me  (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

        1%2FR = 1%2F30 + 1%2Fx.


     It gives you an equation to find x

        1%2F3 = 1%2F30 + 1%2Fx,


     which implies

        1%2Fx = 1%2F3 - 1%2F30,   or

        1%2Fx = 10%2F30 - 1%2F30 = 9%2F30 = 3%2F10.


     Hence,  x = 10%2F3 ohms = 3.333 ohms.      ANSWER



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


         1%2FM = %281%2F2%29%2A%281%2Fa+%2B+1%2Fb%29.


     From this formula,


          M = 2%281%2F%281%2Fa+%2B+1%2Fb%29%29 = %282ab%29%2F%28a+%2B+b%29.    ANSWER


Solved and explained.


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