A metallic wire of resistance `12Omega` is bent of form a square. The resistance between two diagonal points would be

Options

A. `12Omega`
B. `24Omega`
C. `6Omega`
D. `3Omega`

Explanation

To find the resistance between two diagonal points of a square formed by bending a metallic wire of resistance \( 12 \, \Omega \), we can follow these steps:

### Step 1: Understand the Length of the Wire
The total resistance of the wire is given as \( 12 \, \Omega \). When the wire is bent into a square shape, the length of each side of the square can be determined.

Let the total length of the wire be \( L \). Since the wire is bent into a square, the length of each side of the square will be:
\[ \text{Length of one side} = \frac{L}{4} \]

### Step 2: Calculate the Resistance of Each Side
The resistance of a segment of wire is given by the formula:
\[ R = \frac{\rho L}{A} \]
where \( \rho \) is the resistivity, \( L \) is the length, and \( A \) is the cross-sectional area.

Since the total resistance of the wire is \( 12 \, \Omega \), and the wire is now divided into four equal segments (one for each side of the square), the resistance of each side of the square will be:
\[ R_{\text{side}} = \frac{R_{\text{total}}}{4} = \frac{12 \, \Omega}{4} = 3 \, \Omega \]

### Step 3: Analyze the Configuration of the Square
When we look at the square, we need to find the equivalent resistance between two opposite corners (diagonal points).

### Step 4: Identify the Series and Parallel Connections
From one corner to the opposite corner, the current can travel through two paths:
1. From the first corner to the second corner (through two sides in series).
2. From the first corner to the third corner (through the other two sides in series).

Each path consists of two resistors in series:
\[ R_{\text{path}} = R_{\text{side}} + R_{\text{side}} = 3 \, \Omega + 3 \, \Omega = 6 \, \Omega \]

### Step 5: Calculate the Equivalent Resistance
Now, we have two paths, each with a resistance of \( 6 \, \Omega \), connected in parallel. The equivalent resistance \( R_{\text{eq}} \) for two resistors in parallel is given by:
\[ \frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} \]
Substituting the values:
\[ \frac{1}{R_{\text{eq}}} = \frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3} \]
Thus,
\[ R_{\text{eq}} = 3 \, \Omega \]

### Conclusion
The equivalent resistance between the two diagonal points of the square formed by the wire is:
\[ \boxed{3 \, \Omega} \]