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

(D) xy / (x + y)

Step-by-step explanation:

To find r in terms of x and y

Given,

two resistors with resistances x and y are connected in parallel r is the combined resistance of these two resistors the reciprocal of r is equal to the sum of the reciprocals of x and y

Then,

1/r = 1/x + 1/y

1/r = (y + x) / xy

Find the reciprocal of both sides

r = xy / (x + y)

The right answer is option (D) xy / (x + y)