A uniform conducting wire of length `12a` and resistance R is wound up as a current carrying coil in the shape of (i) an equilateral triangle of side a, (ii) a square of sides a and, (iii) a regular hexagon of sides a. The coil is connected to a voltage source `V_0`. Find the magnetic moment of the coils in each case.

Explanation

To solve the problem of finding the magnetic moment of a current-carrying coil in the shape of an equilateral triangle, a square, and a regular hexagon, we will proceed step by step.

### Step 1: Determine the Number of Turns for Each Shape
The total length of the wire is given as \(12a\).

1. **Equilateral Triangle**:
- The perimeter of the triangle is \(3a\).
- Number of turns \(n\) for the triangle:
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