The resistance of a 10 m long copper wire is R ohm. What will be the resistance of a 5 m long copper wire?

Correct option is A

The correct answer is (A) 0.5R ohm.

Explanation:

The resistance of a wire is given by the formula:

​$$R=\rho \frac{L}{A}$$​​

Where:

• ρ = Resistivity of the material,
• L = Length of the wire,
• A= Cross-sectional area of the wire.

Given:

1. For a 10 m long wire, resistance is R.
2. For a 5 m long wire (same material and cross-sectional area), resistance becomes:

​$$R′= \rho \frac{L'}{A} = \rho \frac{5}{A} = \frac{5}{10} R = 0.5R$$​​

Key Concept:

Resistance is directly proportional to the length of the wire when material and cross-sectional area remain constant.