Science (086) — AI-generated practice question

Total resistance of wire = 12 Ω. When bent into a square, each side has resistance = 12/4 = 3 Ω.

Between two diagonally opposite corners (say A and C), the wire splits into two paths:

• Path 1: A→B→C = 3 + 3 = 6 Ω
• Path 2: A→D→C = 3 + 3 = 6 Ω

These two 6 Ω resistors are in parallel:

$$\frac{1}{R_p} = \frac{1}{6} + \frac{1}{6} = \frac{2}{6}$$

$$R_p = 3 \text{ Ω}$$

The resistance between diagonally opposite corners = 3 Ω.

Source: Chapter 11, Section 11.6 (Resistance of a System of Resistors)

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• First find resistance of each side by dividing total resistance by 4.
• Identify the two parallel paths between opposite corners (each path has 2 sides in series = 6 Ω).
• Apply the parallel combination formula. Examiners award marks for: correctly finding each side's resistance, correctly identifying series/parallel arrangement, and the final calculation.