# Problem №3 (10 points)

The circuit diagram shown is composed of identical resistors. If point $A$ is connected to point $C$, and point $B$ is connected to point $D$, the resistance of the circuit changes by 10 Ohms. Determine the resistance of one resistor. The connections between points were made using zero-resistance jumpers.

![](https://cdn.mathpix.com/cropped/2024_05_06_167c0776c22cdf752babg-06.jpg?height=166&width=1471&top_left_y=1048&top_left_x=87)
# Solution:

If the resistance of one resistor is $R$, then the initial total resistance of the series connection is $3 R$

After the jumpers were activated, we get a parallel connection of three resistors.

In this case, their total resistance is $\frac{R}{3}$

According to the condition: $3 R-\frac{R}{3}=10$

Final result: $R=3.75$ Ohms

#