# Problem № 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 $A C E G$. 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 A and $E$.

![](https://cdn.mathpix.com/cropped/2024_05_06_8b91ba68ee8c87ac0dd6g-1.jpg?height=603&width=646&top_left_y=1309&top_left_x=725)
# Answer: 0.94 Ohms

## Solution and grading criteria:

The resistance of a resistor is proportional to its length.

![](https://cdn.mathpix.com/cropped/2024_05_06_8b91ba68ee8c87ac0dd6g-2.jpg?height=591&width=974&top_left_y=190&top_left_x=564)

Its resistance: $\quad R=\frac{4+2 \sqrt{2}}{3+3 \sqrt{2}} R_{0} \approx 0.94$ Ohms

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