NEIEP Mechanics Practice Exam

What happens to the total resistance in a wire if its length is doubled?

1. The resistance remains the same

2. The resistance is halved

3. The resistance is doubled

4. The resistance is quadrupled

The correct answer is: The resistance is doubled

Total resistance in a wire is influenced by its length, cross-sectional area, and the material's resistivity. The relationship can be described 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, and \( A \) is the cross-sectional area. When the length of the wire is doubled, the new length becomes \( 2L \). Plugging this into the formula leads to: \[ R' = \frac{\rho \cdot (2L)}{A} = 2 \cdot \frac{\rho \cdot L}{A} = 2R \] This shows that the resistance increases in direct proportion to the length of the wire. Therefore, if the length is doubled, the total resistance is also doubled. This is why selecting the option indicating that the resistance is doubled is accurate. In contrast, resistance remaining the same, being halved, or quadrupled would not align with the established principles of how resistance is affected by physical dimensions of the material in question.