Question

The total Resisitance of 2 Resistors when connected in series is 9 ohm and when connected in parallel@ their total resistance becomes 2 ohm. Find the value of each resistance.

Answer 1

Dear Student,

The computation is expression below,

$$\begin{gathered} seriesconnection, \\ x+y=9\to eq.\left(1\right) \\ parallelconnection, \\ \frac{1}{x}+\frac{1}{y}=2\Rightarrow \frac{xy}{x+y}=2\to eq.\left(2\right) \\ plugeq.\left(1\right)in\left(2\right)gives, \\ \frac{xy}{9}=2\Rightarrow xy=18 \\ x=\frac{18}{y}\to eq.\left(3\right) \\ nowplugeq.\left(3\right)in\left(1\right)gives, \\ \frac{18}{y}+y=9 \\ 18+y^2=9y \\ {y}^2-9y+18=0 \\ solvinggives, \\ 3ohmand6ohm \end{gathered}$$

Regards.