Question

When a wire is cut, its resistance becomes?

Answer 1

When a wire is cut, its resistance theoretically becomes infinite. Here’s a detailed explanation of why this happens:

### Understanding Wire Resistance

1. **Resistance Basics:**
   The resistance \( R \) of a wire is determined by its material properties and physical dimensions. According to Ohm’s Law, resistance is given by:
   \[
   R = \frac{\rho L}{A}
   \]
   where:
   - \( \rho \) is the resistivity of the material (a property that depends on the material type),
   - \( L \) is the length of the wire,
   - \( A \) is the cross-sectional area of the wire.

2. **Impact of Cutting the Wire:**
   - **Length of the Wire:** When a wire is cut, it effectively divides the wire into two separate pieces. The original wire’s length \( L \) is split into two segments, but for each segment, the length of each piece becomes shorter. However, the most critical point is that there is now an interruption in the continuity of the wire.
   - **Continuity and Circuit Path:** For a wire to conduct electricity, it must provide a continuous path for the flow of electric current. When the wire is cut, this path is broken, meaning that there is no longer a complete circuit through that segment of the wire.

3. **Infinite Resistance:**
   - **Open Circuit Condition:** When the wire is cut, the two ends of the wire are no longer connected. This situation is analogous to an open circuit where no current can flow through the cut section. In terms of resistance, an open circuit has infinite resistance because there is no path for current to travel through. Therefore, the resistance of the cut wire is considered infinite.
   - **Practical Considerations:** In practical scenarios, while the resistance may approach infinity due to the interruption in the circuit, it’s also worth noting that there could be a small amount of resistance associated with the wire ends or connections if they are physically altered or damaged. However, for all intents and purposes, the resistance of a wire that has been cut is treated as infinite.

### Summary

In summary, when a wire is cut, it no longer provides a complete path for electrical current to flow, and thus its resistance becomes effectively infinite. This is due to the fact that an open circuit has no continuous path for current, resulting in infinite resistance in the context of electrical circuits.

Answer 2

When a wire is cut, its resistance essentially becomes infinite. Here's why:

1. **Resistance Concept**: Resistance (\( R \)) of a wire is determined by the formula:
   \[
   R = \rho \frac{L}{A}
   \]
   where \( \rho \) is the resistivity of the material, \( L \) is the length of the wire, and \( A \) is the cross-sectional area of the wire.

2. **Effect of Cutting**:
   - **Before Cutting**: When the wire is intact, it has a finite resistance depending on its length and cross-sectional area.
   - **After Cutting**: Cutting the wire splits it into two or more segments. For each segment, the resistance can still be calculated using the formula above. However, in the context of a complete electrical circuit, cutting the wire breaks the continuity of the circuit. As a result, there is no continuous path for current to flow through the wire.

3. **Infinite Resistance**: Since current cannot flow through an open circuit (caused by cutting the wire), the resistance of the open circuit is considered infinite. This is because an infinite resistance would result in zero current flow, which is consistent with the behavior of an open circuit.

In summary, when a wire is cut, the resistance of the wire in the context of a circuit becomes infinite because the circuit is open and current cannot flow through it.