Combination of Resistors: Practice Problem & Solution
When a wire of uniform cross-section $a$, length $l$ and resistance $R$ is bent into a complete circle, resistance between two of diametrically opposite points will be: (2005)
Solution Explained:
To solve this problem, we apply the core principles of Combination of Resistors. Understanding the underlying formula is key to arriving at the correct answer below:
The wire is divided into two equal semicircular parts, each having a resistance of $R/2$. Since these two parts are connected in parallel across diametrically opposite points, the equivalent resistance is $R_{eq} = \frac{(R/2) \times (R/2)}{(R/2) + (R/2)} = R/4$.
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