QQuestion
A thin wire of resistance 4 Ω is bent to form a circle. Find the resistance across any diameter.
✓Answer
Resistance of the complete wire = 4 Ω
The wire is bent into a circle.
Therefore, the resistance of each semicircle = 4 ÷ 2 = 2 Ω
The two semicircles are connected in parallel between the ends of the diameter.
Equivalent resistance = \frac{R_1 \times R_2}{R_1 + R_2}
= \frac{2 \times 2}{2 + 2}
= \frac{4}{4}
= 1 Ω
Hence, the resistance across any diameter is 1 Ω.
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