Hi There,
Even after reading the explanation I am having some trouble figuring out this one...can anyone please help?
There are 2 resistors x and y connected in parallel. In this case, if r is the combined resistance of these two resistors, then the reciprocal of r is equal to the sum of the reciprocals of x and y. what is r in terms of x and y? #230 pg 262 OG 11th
r=x+y/xy
Thanks!!
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- RonPurewal
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Remember that 'reciprocal of X' translates as '1 over X', or 'X flipped' if X is itself a fraction.
Using that definition, we can turn the original statement into
1/r = 1/x + 1/y
You have two options at this point:
(1) Make a common denominator for the right side NOW, giving 1/r = y/xy + x/xy --> 1/r = (x+y)/xy. Therefore, since r is the reciprocal (flipped version) of 1/r, we have r = xy/(x+y).
(2) Flip both sides of the equation NOW, giving r = 1/(1/x + 1/y). If you multiply the top and bottom of this complex fraction by the common denominator xy/1, you get r = xy/(xy/x + xy/y) = xy/(y+x) = xy/(x+y).
--
Notice that you have actually given the reciprocal of the correct answer (rather than the correct answer itself), a fact that may be contributing to your trouble with this problem!
Using that definition, we can turn the original statement into
1/r = 1/x + 1/y
You have two options at this point:
(1) Make a common denominator for the right side NOW, giving 1/r = y/xy + x/xy --> 1/r = (x+y)/xy. Therefore, since r is the reciprocal (flipped version) of 1/r, we have r = xy/(x+y).
(2) Flip both sides of the equation NOW, giving r = 1/(1/x + 1/y). If you multiply the top and bottom of this complex fraction by the common denominator xy/1, you get r = xy/(xy/x + xy/y) = xy/(y+x) = xy/(x+y).
--
Notice that you have actually given the reciprocal of the correct answer (rather than the correct answer itself), a fact that may be contributing to your trouble with this problem!
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