Solve problem `15` if the length of rod is `2L` and resistance `2r` and it is rotating about its center. Both ends of the rod now touch the conducting ring.

Explanation

To solve the problem, we need to find the current flowing through the resistance when a rod of length \(2L\) and resistance \(2r\) is rotating about its center. Both ends of the rod touch a conducting ring.

### Step-by-Step Solution:

1. **Identify the Length and Resistance of the Rod:**
- The total length of the rod is \(2L\).
- Since the rod is rotating about its center, each half of the rod will have a length of \(L\).
- The total resistance of the rod is given as \(2r\). Since the rod is uniform, the resistance of each half will be \(r\).
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