The equivalent resistance between points A and B in the given network is

The circuit can be analyzed step-by-step to determine the equivalent resistance between A and B. The process involves simplifying the resistors in the network by combining them in series and parallel as applicable. Here is the step-by-step solution:

Step 1: Combine R₁ and R₂ in Series

When resistors are connected in series, their resistances add up:

R_eq1 = R₁ + R₂ = 5 Ω + 5 Ω = 10 Ω

Step 2: Combine R_eq1 and R₃ in Parallel

For resistors in parallel, the equivalent resistance is calculated using the formula:

R_eq2 = (R_eq1 × R₃) / (R_eq1 + R₃)

Substituting the values:

R_eq2 = (10 × 10) / (10 + 10) = 100 / 20 = 5 Ω

Step 3: Combine R_eq2 and R₄ in Series

Adding the resistances in series:

R_eq3 = R_eq2 + R₄ = 5 Ω + 5 Ω = 10 Ω

Step 4: Combine R_eq3 and R₅ in Parallel

Applying the parallel resistance formula:

R_eq4 = (R_eq3 × R₅) / (R_eq3 + R₅)

R_eq4 = (10 × 10) / (10 + 10) = 100 / 20 = 5 Ω

Step 5: Combine R_eq4 and R₆ in Series

Adding the resistances in series:

R_eq5 = R_eq4 + R₆ = 5 Ω + 5 Ω = 10 Ω

Step 6: Combine R_eq5 and R₇ in Parallel

Using the parallel resistance formula:

R_eq6 = (R_eq5 × R₇) / (R_eq5 + R₇)

R_eq6 = (10 × 10) / (10 + 10) = 100 / 20 = 5 Ω

Step 7: Combine R_eq6 and R₈ in Series

Adding the resistances in series:

R_eq7 = R_eq6 + R₈ = 5 Ω + 5 Ω = 10 Ω

Step 8: Combine R_eq7 and R₉ in Parallel

For the final step, calculate the equivalent resistance:

R_eq = (R_eq7 × R₉) / (R_eq7 + R₉)

R_eq = (10 × 10) / (10 + 10) = 100 / 20 = 5 Ω

Final Answer

The equivalent resistance between A and B is 5 Ω.