Question

Find the equivalent resistance between two ends of the following circuit:

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

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

Let's simplify the given circuit.
The circuit consists of three resistors, each with a resistance of $ r/3 $. Let's label them $ R_1 $, $ R_2 $, and $ R_3 $.

We know:

$ \frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} $

$ \Rightarrow \frac{1}{R_p} = \frac{3}{r} + \frac{3}{r} + \frac{3}{r} = \frac{9}{r} $

$ \Rightarrow R_p = \frac{r}{9} $

Final Answer:
The final answer is $ \boxed{r/9} $.