Question

In the circuit below, resistors Ry and R2 are in parallel. What is the equivalent resistance?

Answer 1

According to the formula for the total resistance of an arrangement of resistors in parallel:

`\frac{1}{R_{\text{tot}}}=(1)/(R_1)+(1)/(R_2)`

Substitute the values R_1=30Ω and R_2=20Ω to find the total resistance:

`\begin{gathered} \Rightarrow(1)/(R_(tot))=(1)/(30\Omega)+(1)/(20\Omega) \\ =(20\Omega+30\Omega)/((30\Omega)(20\Omega)) \\ =(50\Omega)/(600\Omega^2) \\ =(1)/(12\Omega) \end{gathered}`

Solve for R_tot:

`\begin{gathered} \frac{1}{R_{\text{tot}}}=(1)/(12\Omega) \\ \Rightarrow R_(tot)=12\Omega \end{gathered}`

Therefore, the equivalent resistance is:

`12\Omega`