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Equivalent resistance between A and B

Short answer

The wire shorts the 24 Ω resistor, so it carries no current. The two 8 Ω resistors are in parallel between terminals A and B. Equivalent resistance RAB = 8 Ω || 8 Ω = 4 Ω.

Find the equivalent resistance between A and B for the network shown in figure below. [Figure: 24 Ω resistor across the top; two 8 Ω resistors in the middle meeting at terminal A; terminal B at the bottom.]

Reading the figure

The 24 Ω and the 8 Ω pair are connected between the left and right nodes X and Y. The outer wire joins X to Y directly and terminal B is on this wire, so X, Y and B are all the same point. Terminal A is the middle point between the two 8 Ω resistors.

   X ---[24]--- Y        X = Y = B (joined by the wire)
   X --[8]--A--[8]-- Y

Analysis

  • The 24 Ω resistor is connected across X and Y, which are shorted together, so it carries no current and can be ignored.
  • Between A and B: the left 8 Ω (A to X) and the right 8 Ω (A to Y) both end at point B.

R_AB = 8 ∥ 8 = (8 × 8)/(8 + 8) = 4 Ω

Answer: R_AB = 4 Ω

✓ Answer checked by Claude Opus 5.5 (high effort)

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