Question

When two resistors are connected in series, their effective resistance is $80\Omega$. When they are connected in parallel, their effective resistance is $20\Omega$. What are the values of two resistances?

Answer 1

Let the two resistances be $R_1$ and $R_2$.

Series connection $R_s=R_1+R_2$

Or $80=R_1+R_2$

$⟹R_1=80-R_2$

Parallel connection :

$R_p=\frac{R_1{R}_2}{R_1+R_2}$

Or $20=\frac{R_1(80-R_1)}{80}$

Or $R_1^2+80R_1-1600=0$

$⟹R_1=40\Omega$

So, $R_2=80-40=40\Omega$