Ohm's Law and Current-Voltage Graphs

Push more voltage across a resistor and you push more current through it, in direct proportion. Voltage is the electrical push per charge, resistance is how hard the material fights back against charge flow, and current is the result of those two fighting it out: I = V/R. Double the voltage with the same resistor, and you double the current. The resistor itself does not change: its resistance stays fixed as long as its temperature and material stay the same, so it responds the same way no matter how much voltage you throw at it.

Graph current on the vertical axis against voltage on the horizontal axis for an ordinary resistor, and you get a straight line through the origin. The steepness of that line is 1/R: a steep line means a small resistance, since it takes very little voltage to drive a lot of current. A shallow line means a large resistance. Flip the axes and graph voltage against current instead, and the slope becomes R directly. Either way, the straight line is the signature of a resistor that obeys Ohm's law.

Not everything behaves this way. A diode, a lightbulb filament that heats up, or a transistor gives a curved I-V graph because its resistance changes with voltage or temperature. Ohm's law is really a description of how certain materials happen to behave, not a conservation principle like charge conservation, which must hold in every circuit no matter what the components are made of. This distinction matters once you start combining resistors in series and parallel, where Ohm's law applies locally to each resistor even as total current and voltage rearrange themselves around the circuit.