In an electric circuit, two resistors with resistances x and y are 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?
(A) xy
(B) x + y
(C) 1/(x + y)
(D) xy/(x + y)
(E) (x + y)/xy
The OA is the option D.
I am really confused here. Experts, can you give me your explanation here? Thanks.
In an electric circuit, two resistors with resistances . . .
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The reciprocal of r is equal to the sum of the reciprocals of x and yM7MBA wrote:In an electric circuit, two resistors with resistances x and y are 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?
(A) xy
(B) x + y
(C) 1/(x + y)
(D) xy/(x + y)
(E) (x + y)/xy
So, 1/r = 1/x + 1/y
We must solve this equation for r.
Take: 1/r = 1/x + 1/y
Rewrite the right side with a COMMON DENOMINATOR of xy: 1/r = y/xy + x/xy
Combine the two terms to get: 1/r = (y + x)/xy
Since we have two equivalent fractions, their reciprocals will also be equal.
That is: r/1 = xy/(y + x)
Or, r = xy/(y + x)
Answer: D
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We are given that the reciprocal of r is equal to the sum of the reciprocals of x and y. Thus we can say:M7MBA wrote:In an electric circuit, two resistors with resistances x and y are 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?
(A) xy
(B) x + y
(C) 1/(x + y)
(D) xy/(x + y)
(E) (x + y)/xy
1/r = 1/x + 1/y
Getting a common denominator for the right side of the equation, we have:
1/r = y/xy + x/xy
1/r = (y + x)/xy
If we reciprocate both sides of the equation, we have:
r = xy/(y+x)
Answer: D
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