When resistors 1 and 2 are connected in series, the equivalent resistance is 14.0 Ω.

Question

When resistors 1 and 2 are connected in series, the equivalent resistance is 14.0 Ω. When they are connected in parallel, the equivalent resistance is 2.62 Ω. What are (a) the smaller resistance and (b) the larger resistance of these two resistors?

Answer 1

Call one of the resistances A, and the other B (which is which matters not).

When two resistors are in series, the equivalent resistance is the sum of the two resistors. Therefore,

A+B=14

When two resistors are in parallel, the inverse of the equivalent resistance is the sum of the inverses of the two resistances. So

1/A+1/B=1/2.62

This is a system of equations. You can use whatever technique you please. Probably you'll want to solve the first equation for one of the resistances, and substitute into the other equation and solve.

You should get

7 - 2*sqrt(77)/5

7+ 2*sqrt(77)/5