Respuesta :
As per the question, the resistor system contains two resistors.
The two resistors are denoted as [tex]r_{1}\ and\ r_{2}\ respectively[/tex]
We are asked to calculate the effective resistance in terms of [tex]r_{1}\ and\ r_{2}\ respectively[/tex]
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 [tex]r= r_{1} +r_{2}[/tex] [ans]
CASE-2: Let the resistors are connected in parallel.
The effective resistance is calculated as follows-
[tex]\frac{1}{r}= \frac{1}{ r_{1}}+ \frac{1}{r_{2}}[/tex]
[tex]=\frac{r_{1}+ r_{2}} {r_{1} r_{2}}[/tex]
⇒ [tex]r =\frac{r_{1} r_{2}} { r_{1} +r_{2}}[/tex] [ans]
