A technician has only two resistance coils. By using them singly in series or in parallel, he is able to obtain the resistance 3,4,12 and 16 ohms. The resistance of two coils are.

$With two resis\tan ce R_1 and R_2 we have the three possible combinations possible$

$\text{ (1) }{R}_1\text{ or }{R}_2\text{ if they are used individually }$…… (1)

$\text{ let }{R}_2\text{ be the larger of the two. }$

$$\begin{gathered} \text{ (2) }\frac{R_1{R}_2}{R_1+R_2}\text{ if used in parallel } \\ \text{ This is the smallest value. It is }<R_1\text{ and }<R_2 \end{gathered}$$

$$\begin{gathered} \text{ (3) }\left(R_1+R_2\right)\text{ if used in series. } \\ \text{ This is the largest value. So it is }>R_1\text{ and }>R_2 \\ \text{ Hence from the given value } \\ \left({\mathrm{R}}_1+{\mathrm{R}}_2\right)=16\mathrm{\Omega } \\ \frac{{\mathrm{R}}_1{\mathrm{R}}_2}{\left({\mathrm{R}}_1+{\mathrm{R}}_2\right)}=3\mathrm{\Omega } \\ \text{ So, }{\mathrm{R}}_1\text{ and }{\mathrm{R}}_2\text{ are }4\mathrm{\Omega }\text{ and }12\mathrm{\Omega }\text{ respectively. } \end{gathered}$$