What is the equivalent resistance between two diametrically opposite points A and B on a uniform circular wire ring of total resistance R?
Answer and explanation
Correct answer: D. R / 4
.
- Step 1: A uniform wire ring of total resistance is cut into two equal semicircular halves by any two diametrically opposite points and .
- Step 2: Each semicircular half contains half of the wire length, so each branch has resistance: .
- Step 3: Between points and , these two semicircular branches are connected in parallel.
- Step 4: The equivalent parallel resistance is:
Answer
R / 4
Why not the others: 'R / 2' is the resistance of one individual semicircle, not the parallel combination; 'R' is the total resistance of the unbent wire; '2 R' would be a series combination of two rings.
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