Problem No. 5 (10 points)

When constructing this structure, a homogeneous wire of constant cross-section was used. It is known that points $B, D, F$ and $H$ are located equally at the midpoints of the corresponding sides of the square ACEG. The resistance of segment $A B$ is $R_{0}=1 \Omega$. Determine the resistance of the entire structure if it is connected to the electrical circuit at points C and $G$.

![](https://cdn.mathpix.com/cropped/2024_05_06_8b91ba68ee8c87ac0dd6g-5.jpg?height=554&width=557&top_left_y=1231&top_left_x=778)
Answer: 2 Ohms

## Solution and grading criteria:

The resistance of a resistor is proportional to its length.

Taking this into account, the proposed circuit can be replaced by an equivalent one:

![](https://cdn.mathpix.com/cropped/2024_05_06_8b91ba68ee8c87ac0dd6g-5.jpg?height=337&width=1148&top_left_y=2259&top_left_x=474)

Its resistance: $\quad R=2 R_{0} \approx 2$ Ohms

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