To find the equivalent resistance of the circuit between terminals A and B, we can use the principles of series and parallel resistor combinations. Let's analyze the circuit step by step:

Step 1: Identify Series and Parallel Combinations

Looking at the circuit:

• R2, R3, and R4 are in parallel.
• R5 is in series with the parallel combination of R2, R3, and R4.
• R6, R7, R9, and R10 are in series.
• R8 is in parallel with the series combination of R6, R7, R9, and R10.
• Finally, the combination of R5 (with its associated parallel combination) and R1 is in parallel with the combination of R8 (with its associated series combination).

Step 2: Calculate Parallel and Series Combinations

1. Calculate the parallel combination of R2, R3, and R4:

   $R_{234} = \left( \frac{1}{R2} + \frac{1}{R3} + \frac{1}{R4} \right)^{-1} = \left( \frac{1}{4} + \frac{1}{4} + \frac{1}{6} \right)^{-1}$

2. Combine R5 in series with R234:

   $R_{5+234} = R5 + R_{234}$

3. Calculate the series combination of R6, R7, R9, and R10:

   $R_{67910} = R6 + R7 + R9 + R10$

4. Calculate the parallel combination of R8 with R67910:

   $R_{8+67910} = \left( \frac{1}{R8} + \frac{1}{R67910} \right)^{-1}$

5. Finally, calculate the parallel combination of R1 with the total resistance from above:

   $R_{AB} = \left( \frac{1}{R1} + \frac{1}{R5+234} + \frac{1}{R8+67910} \right)^{-1}$

Step 3: Perform the Calculations

Let me calculate the equivalent resistance between terminals A and B.The equivalent resistance of the circuit as seen from terminals A and B is approximately $4.36 \, \Omega$.

Would you like more details or have any additional questions? Here are some related questions you might find interesting:

1. How would the equivalent resistance change if resistor $R1$ was removed?
2. What is the effect of increasing $R10$ on the overall resistance?
3. Can you determine the current flowing through each resistor if a voltage source was connected across terminals A and B?
4. How would you simplify this circuit if some resistors had equal values?
5. What happens to the equivalent resistance if $R8$ is short-circuited?

Tip: When dealing with complex resistor networks, breaking down the circuit into smaller series and parallel combinations can simplify the analysis and help avoid mistakes.