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. $\frac{1}{x+y}$
• D. $\frac{xy}{x+y}$
• E. $\frac{x+y}{xy}$

Answer 1

The correct option is D $\frac{xy}{x+y}$

Given 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 it means

$\frac{1}{r}=\frac{1}{x}+\frac{1}{y}$

$\frac{1}{r}=\frac{x+y}{xy}r=\frac{xy}{x+y}$

So correct answer will be option D