Science (086) — CBSE Class 10 board question

(D) 6 Ω

From point 1 to point 2: one path has 2 resistors (12+12 = 24 Ω) and the other path also has 2 resistors (12+12 = 24 Ω). These two paths are in parallel: $R = \dfrac{24 \times 24}{24+24} = \mathbf{9\ \Omega}$.

(C) 9 Ω

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Points 1 and 2 are at diagonally opposite corners of the square. Current can travel two ways:

• Path 1 (A→B→2): two 12 Ω resistors in series = 24 Ω
• Path 2 (A→D→C→2 or equivalent): two 12 Ω resistors in series = 24 Ω

Both paths (24 Ω each) are in parallel between points 1 and 2:
$$R = \frac{24 \times 24}{24 + 24} = \frac{576}{48} = 9\ \Omega$$

The correct answer is (C) 9 Ω. (Option D, 6 Ω, is a common error from miscounting resistors in each path.)