What is the relationship between voltage and current in a fixed resistor?

The relationship between voltage and current in a fixed resistor is described by Ohm's Law, which states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points, provided the temperature remains constant. This means that if you increase the voltage applied to the resistor, the current flowing through it will also increase, as long as the resistance remains constant.

This direct proportionality indicates that if you were to graph the current (I) against the voltage (V) for a fixed resistor, you would see a straight line passing through the origin. The slope of this line is equal to the resistance (R) of the resistor, given by the formula V = I × R. Therefore, as you adjust the voltage, the current adjusts accordingly, maintaining this linear relationship.

In contrast, other relationships indicated in the choices, such as inversely proportional, exponential, or no relationship, do not hold true under normal conditions for a linear resistor. Inversely proportional would imply that as one increases, the other decreases, the exponential relationship suggests a curve rather than a straight line, and stating there is no relationship contradicts basic electrical principles observed in resistive materials.