When the cross-sectional area of a conductor doubles, what happens to its resistance?

When the cross-sectional area of a conductor doubles, what happens to its resistance?

• A. Resistance doubles
• B. Resistance is halved
• C. Resistance remains the same
• D. Resistance is quadrupled

Answer: (B)

When the cross-sectional area of a conductor increases, the resistance of that conductor decreases. The relationship between resistance (R), resistivity (ρ), length (L), and cross-sectional area (A) is described by the formula: \[ R = \frac{\rho L}{A} \] From this equation, it is clear that resistance is inversely proportional to the area of the conductor. Therefore, if the cross-sectional area of the conductor doubles, the resistance will be halved because the increase in area allows more path for the electric current to flow through, reducing the resistance. This is why option indicating that the resistance is halved is the correct answer. The other options do not align with the physical principles of how resistance behaves in relation to the geometry of a conductor.

When the cross-sectional area of a conductor increases, the resistance of that conductor decreases. The relationship between resistance (R), resistivity (ρ), length (L), and cross-sectional area (A) is described by the formula:

[ R = \frac{\rho L}{A} ]

From this equation, it is clear that resistance is inversely proportional to the area of the conductor. Therefore, if the cross-sectional area of the conductor doubles, the resistance will be halved because the increase in area allows more path for the electric current to flow through, reducing the resistance.

This is why option indicating that the resistance is halved is the correct answer. The other options do not align with the physical principles of how resistance behaves in relation to the geometry of a conductor.