Question

When resistors 1 and 2 are connected in series, the equivalent resistance is 18.4 Ω. When they are connected in parallel, the equivalent resistance is 3.50 Ω. What are (a) the smaller resistance and (b) the larger resistance of these two resistors?

Answer 1

Let us say series arrangement to be (1) and parallel arrangement to be (2)

So, equivalent resistance in both the arrangements are

(1) R₁+ R₂ = 18.4
(2) R₁*R₂/(R₁ +R₂) = 3.5

from(1);
(3) R₂ = 18.4 - R₁
substituting in (2);
R₁*(18.4 - R₁)/(R₁+18.4 - R₁) = 3.5
(18.4*R₁ - R₁²)/(R₁ +18.4 - R₁) = 3.5
(18.4*R₁ - R₁²)/(18.4) = 3.5
18.4*R₁ - R₁² = 18.4*3.5
18.4*R₁ - R₁² = 64.4
R₁² - 18.4*R₁ +64.4 = 0

by quadratic formula;
R₁ = 13.698
using (3);
R₂ = 4.701

R₁ = 13.698 ....... Answer B
R₂ = 4.701........ Answer A