Question

When A wire of resistance 12 is cut into three?

Answer 1

When a wire with a resistance of \( R = 12 \, \Omega \) is cut into three equal parts, the resistance of each part can be calculated using the formula for resistance in a uniform wire, which states that the resistance is directly proportional to its length and inversely proportional to its cross-sectional area.

### Step-by-Step Calculation

1. **Total Resistance of the Wire**:
   The original wire has a resistance of \( R_{\text{total}} = 12 \, \Omega \).

2. **Length of Each Part**:
   When the wire is cut into three equal parts, the length of each part is \( L' = \frac{L}{3} \), where \( L \) is the original length of the wire.

3. **Resistance of Each Part**:
   Since resistance is directly proportional to length, the resistance of each of the three parts will be:
   \[
   R' = \frac{R_{\text{total}}}{n}
   \]
   where \( n \) is the number of pieces the wire is cut into.

   For our case:
   \[
   R' = \frac{12 \, \Omega}{3} = 4 \, \Omega
   \]

### Conclusion
Each of the three pieces of wire will have a resistance of \( 4 \, \Omega \).

### Summary:
- **Original Wire Resistance**: \( 12 \, \Omega \)
- **Resistance of Each Cut Piece**: \( 4 \, \Omega \) (after cutting into three equal parts)

Answer 2

When a wire of resistance \( R \) is cut into multiple pieces, the resistance of each piece depends on how the wire is divided. Let’s go through the scenario where a wire of resistance 12 ohms is cut into three equal parts.

### Case 1: Wire Cut into Three Equal Parts

1. **Original Wire Resistance**: \( R = 12 \) ohms.

2. **Length of Each Part**: If the wire is cut into three equal lengths, the length of each part is one-third of the original wire.

3. **Resistance of Each Part**:
   - Resistance \( R \) of a wire is proportional to its length \( L \). If the length is reduced to \( \frac{1}{3} \), the resistance of each part will be \( \frac{1}{3} \) of the original resistance.
   - Therefore, the resistance of each new wire \( R_{new} \) will be:
     \[
     R_{new} = \frac{R}{3} = \frac{12 \text{ ohms}}{3} = 4 \text{ ohms}
     \]

### Case 2: Wire Cut into Three Parts of Different Lengths

If the wire is cut into three parts of different lengths, you would need to know the exact lengths of each piece to calculate their resistances. The resistance of each part can be calculated using the formula:
\[
R_{part} = R_{original} \times \frac{L_{part}}{L_{original}}
\]
where \( L_{part} \) is the length of the part and \( L_{original} \) is the total length of the original wire.

### Summary

- **When a wire of 12 ohms resistance is cut into three equal parts**, each part will have a resistance of 4 ohms.