Question

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

Answer 1

(D) xy/(x + y)

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)