To find the equivalent resistance between points A and B, we need to analyze the given resistor network. The configuration is a combination of series and parallel resistances.
Let's break it down step by step:
First, observe the resistors between A and B. Notice that there are several 5 Ω and 10 Ω resistors forming both series and parallel combinations.
The top part of the network (two 5 Ω resistors) is in series, so their total resistance is:
R_{\text{top}} = 5 + 5 = 10 \, \Omega.
This 10 \, \Omega is in parallel with the middle 10 Ω resistor:
\frac{1}{R_{\text{parallel}}} = \frac{1}{10} + \frac{1}{10},
which simplifies to:
R_{\text{parallel}} = 5 \, \Omega.
Next, consider the two bottom 5 Ω resistors in series giving:
R_{\text{bottom}} = 5 + 5 = 10 \, \Omega.
This 10 \, \Omega is then in parallel with the middle 10 Ω:
\frac{1}{R_{\text{bottom}}} = \frac{1}{10} + \frac{1}{10},
which again simplifies to:
R_{\text{bottom}} = 5 \, \Omega.
Finally, these two equivalent 5 Ω resistors (from the top parallel part and the bottom parallel part) are in series:
R_{\text{total}} = 5 + 5 = 10 \, \Omega.
So, the correct answer is 5 Ω.
Conclusion: Therefore, the equivalent resistance between points A and B is indeed 5 Ω, confirming the given answer.
