The equivalent resistance between the points A and B in the following circuit is x/5 Ω. The value of x i $s ________.$

Question

The equivalent resistance between the points A and B in the following circuit is x/5 Ω. The value of x i s ________.

G1 Physics · Accepted Answer

Use a 1 V test source between A and B. Let V(A) = 1 V, V(B) = 0. Let the potential at the upper middle node be V₁ and at the lower middle node be V₂. At the upper node, Kirchhoff's current law gives (V₁-1)/6 +V₁/3 +(V₁-V₂)/3 = 0. Multiplying by 6: V₁-1 +2V₁ +2V₁-2V₂ = 0. Therefore, 5V₁-2V₂ = 1. (1) At the lower node, (V₂-1)/3 +V₂/6 +(V₂-V₁)/3 = 0. Multiplying by 6: 2V₂-2 +V₂ +2V₂-2V₁ = 0. Hence, -2V₁+5V₂ = 2. (2) Solving equations (1) and (2), V₁ = 3/7, V₂ = 4/7. Total current drawn from A is I…