Ohm's law, which states \( V = IR \), applies to ohmic materials where the resistance remains constant regardless of voltage and current. You can't use Ohm's law when dealing with non-ohmic materials, like diodes or transistors, where resistance changes with voltage or current. It also doesn't apply in situations involving superconductors at temperatures below their critical temperature or in circuits with highly variable or reactive components like inductors and capacitors. In such cases, you need to use more complex methods to analyze the behavior of the circuit.