Question

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

Answer 1

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

The two resistors are denoted as $r_{1}\ and\ r_{2}\ respectively$

We are asked to calculate the effective resistance in terms of  $r_{1}\ and\ r_{2}\ respectively$

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  $r= r_{1} +r_{2}$  [ans]

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

The effective resistance is calculated as follows-

                                     $\frac{1}{r}= \frac{1}{ r_{1}}+ \frac{1}{r_{2}}$

                                            $=\frac{r_{1}+ r_{2}} {r_{1} r_{2}}$

                                   ⇒  $r =\frac{r_{1} r_{2}} { r_{1} +r_{2}}$  [ans]