At constant voltage, doubling the resistance halves the current. What is the correct statement?

The correct statement is true because of Ohm's Law, which states that the current (I) flowing through a conductor is directly proportional to the voltage (V) across it and inversely proportional to the resistance (R). The mathematical representation of Ohm's Law is I = V/R.

When voltage is constant, if the resistance is doubled, the formula can be rearranged to show that the new current will be half of the original current. For example, if the original resistance is R, the current is I = V/R. If the resistance is increased to 2R, the new current becomes I' = V/(2R), which simplifies to I' = (1/2)(V/R), demonstrating that the current is halved when the resistance is doubled as long as the voltage remains constant.

This principle is fundamental to both direct current (DC) and alternating current (AC) circuits and is universally applicable, not just limited to a specific type of circuit configuration. Understanding this relationship is crucial for analyzing circuit behavior in various electrical engineering contexts.