If the length of a wire is doubled by taking more of wire, what happens to its resistance?

Answer

To determine what happens to the resistance of a wire when its length is doubled, we can follow these steps:

### Step-by-Step Solution

1. **Understand the Formula for Resistance**:
The resistance \( R \) of a wire is given by the formula:
\[ R = \frac{\rho \cdot L}{A} \]
where:
- \( R \) is the resistance,
- \( \rho \) is the resistivity of the material,
- \( L \) is the length of the wire,
- \( A \) is the cross-sectional area of the wire.

2. **Identify the Changes**:
In this scenario, the length of the wire is doubled. If the original length of the wire is \( L \), the new length \( L' \) will be:
\[ L' = 2L \]

3. **Substitute the New Length into the Resistance Formula**:
We can now substitute the new length into the resistance formula:
\[ R' = \frac{\rho \cdot L'}{A} = \frac{\rho \cdot (2L)}{A} \]

4. **Simplify the Expression**:
Simplifying the expression gives:
\[ R' = 2 \cdot \frac{\rho \cdot L}{A} = 2R \]
where \( R \) is the original resistance of the wire.

5. **Conclusion**:
Therefore, when the length of the wire is doubled, the resistance also doubles. If the original resistance was \( R \), the new resistance \( R' \) will be:
\[ R' = 2R \]

### Final Answer:
When the length of the wire is doubled, its resistance also doubles.

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