In a resistor's current–voltage graph, which statement is correct?

In a resistor's current–voltage graph, which statement is correct?

• A. Current is directly proportional to voltage, giving a straight line through the origin; resistance stays the same
• B. Current is inversely proportional to voltage
• C. The graph is curved
• D. Resistance increases with voltage

Answer: (A)

Current through a resistor that follows Ohm’s law is directly proportional to the voltage across it, with the resistance acting as the constant of proportionality. This means doubling the voltage doubles the current, and on a graph of current versus voltage you get a straight line that passes through the origin. The slope of that line is the resistance, which stays the same as voltage changes (within the resistor’s normal operating range). If the current were inversely proportional to voltage, the graph would curve downward rather than form a straight line. If the graph were curved, the resistor wouldn’t be Ohmic in that region. If the resistance increased with voltage, the line would bend so the slope gets smaller at higher voltages. So the straight line through the origin with constant resistance best describes an ohmic resistor.

Current through a resistor that follows Ohm’s law is directly proportional to the voltage across it, with the resistance acting as the constant of proportionality. This means doubling the voltage doubles the current, and on a graph of current versus voltage you get a straight line that passes through the origin. The slope of that line is the resistance, which stays the same as voltage changes (within the resistor’s normal operating range). If the current were inversely proportional to voltage, the graph would curve downward rather than form a straight line. If the graph were curved, the resistor wouldn’t be Ohmic in that region. If the resistance increased with voltage, the line would bend so the slope gets smaller at higher voltages. So the straight line through the origin with constant resistance best describes an ohmic resistor.