If you double the length of a conductor in a circuit, what happens to the resistance and voltage drop?

If you double the length of a conductor in a circuit, what happens to the resistance and voltage drop?

• A. Resistance remains the same; voltage drop doubles.
• B. Resistance decreases; voltage drop remains constant.
• C. Resistance increases; voltage drop decreases.
• D. Resistance increases proportionally and voltage drop increases accordingly.

Answer: (D)

A conductor’s resistance scales with its length, so doubling the length makes the resistance double. Ohm’s law ties voltage drop to the current through the element: V = I R. If the current through that conductor stays the same, then doubling the resistance doubles the voltage drop across it. So increasing the length increases both the resistance and the voltage drop proportionally. (In a whole circuit, the current can adjust based on the total resistance, but for a given current through the lengthened piece, the drop rises in step with the resistance.)

A conductor’s resistance scales with its length, so doubling the length makes the resistance double. Ohm’s law ties voltage drop to the current through the element: V = I R. If the current through that conductor stays the same, then doubling the resistance doubles the voltage drop across it. So increasing the length increases both the resistance and the voltage drop proportionally. (In a whole circuit, the current can adjust based on the total resistance, but for a given current through the lengthened piece, the drop rises in step with the resistance.)