Question

Find the equivalent resistance between two ends of the following circuit: 
The circuit consists of three resistors, two of \(\frac{r}{3}\) in series connected in parallel with another resistor of \(r\).

• A. \(\frac{r}{6}\)
• B. \(r\)
• C. \(\frac{r}{9}\)
• D. \(\frac{r}{3}\)

Hint:

When combining resistors, always double-check if they are in series or parallel and apply the appropriate formula to find the total resistance.

Answer 1

The Correct Option is D

Step 1: Calculate the series combination of the two \(\frac{r}{3}\) resistors. \[ R_{series} = \frac{r}{3} + \frac{r}{3} = \frac{2r}{3} \] Step 2: Calculate the parallel combination with the \(r\) resistor. \[ R_{parallel} = \left(\frac{1}{\frac{2r}{3}} + \frac{1}{r}\right)^{-1} = \left(\frac{3}{2r} + \frac{1}{r}\right)^{-1} = \left(\frac{5}{2r}\right)^{-1} = \frac{2r}{5} \] Conclusion: The equivalent resistance is \(\frac{r}{3}\).