All else equal, increasing the cross-sectional area A of a conductor will cause Q/t to:

All else equal, increasing the cross-sectional area A of a conductor will cause Q/t to:

• A. Depends on ΔT
• B. Stays the same
• C. Decreases With A
• D. Increases Proportionally With A

Answer: (D)

The total current—the charge flowing per second—scales with how much cross-sectional area there is for the charges to move through. For a conductor with a fixed material and a fixed driving voltage across a given length, the current density J is proportional to the electric field E (Ohm’s law at a point: J = σE). The total current is I = J A, so increasing the cross-sectional area increases the current in direct proportion to A. In other words, doubling the area doubles the amount of charge that can pass per second, as long as the material, length, and applied voltage stay the same. The other options would require changing temperature or imply no change, which isn’t the scenario given.

The total current—the charge flowing per second—scales with how much cross-sectional area there is for the charges to move through. For a conductor with a fixed material and a fixed driving voltage across a given length, the current density J is proportional to the electric field E (Ohm’s law at a point: J = σE). The total current is I = J A, so increasing the cross-sectional area increases the current in direct proportion to A. In other words, doubling the area doubles the amount of charge that can pass per second, as long as the material, length, and applied voltage stay the same. The other options would require changing temperature or imply no change, which isn’t the scenario given.