What is the effective resistance r of the two-resistor system? express the effective resistance in terms of r1 and r2?

As per the question, the resistor system contains two resistors.

The two resistors are denoted as

We are asked to calculate the effective resistance in terms of  

The two resistors can be connected in two ways.

CASE-1: Let the resistors are connected in series.

When the resistors are connected in series, the effective resistance is the algebraic sum of the individual resistors.

Hence, the effective resistance    [ans]

CASE-2: Let the resistors are connected in parallel.

The effective resistance is calculated as follows-

                                   ⇒    [ans]