According to the formula for the total resistance of an arrangement of resistors in parallel:
[tex]\frac{1}{R_{\text{tot}}}=\frac{1}{R_1}+\frac{1}{R_2}[/tex]
Substitute the values R_1=30Ω and R_2=20Ω to find the total resistance:
[tex]\begin{gathered} \Rightarrow\frac{1}{R_{tot}}=\frac{1}{30\Omega}+\frac{1}{20\Omega} \\ =\frac{20\Omega+30\Omega}{(30\Omega)(20\Omega)} \\ =\frac{50\Omega}{600\Omega^2} \\ =\frac{1}{12\Omega} \end{gathered}[/tex]
Solve for R_tot:
[tex]\begin{gathered} \frac{1}{R_{\text{tot}}}=\frac{1}{12\Omega} \\ \Rightarrow R_{tot}=12\Omega \end{gathered}[/tex]
Therefore, the equivalent resistance is:
[tex]12\Omega[/tex]
