Three resistors

You must connect three identical resistors with 12 Ohm resistances to get the resulting resistance gradually) 36 Ohm, b) 4 Ohm and 18 Ohm. Draw a diagram of each circuit.

Correct answer:

a = SSS
b = PPP
c = SPP

Step-by-step explanation:

$$\begin{gathered} R_1=12\Omega \\ {R}_2=R_1+R_1+R_1=12+12+12=36\Omega \\ a=SSS \end{gathered}$$

$$\begin{gathered} 1/R_3=1/R_1+1/R_1+1/R_1=1/12+1/12+1/12=\frac{1}{4}=0.25 \\ {R}_3=1/(1/R_1+1/R_1+1/R_1)=1/(1/12+1/12+1/12)=4\Omega \\ b=PPP \end{gathered}$$

$$\begin{gathered} R_4=R_1+1/(1/R_1+1/R_1)=12+1/(1/12+1/12)=18\Omega \\ c=SPP \end{gathered}$$

Try another example