Here is my simple reasoning. We apply a potential difference across a resistor. All the electrons begin responding. Since it takes time for electrons to respond, our current is not yet fully established. In fact, immediately after we apply the voltage, the current is zero! And yet we have a non-zero V and R. So am I wrong here, or does V sometimes not equal IR?
EDIT: I'm having a bit of an issue here. People want to say that an inductance of zero will allow for instantaneous current initiation, but I wonder. Is it ever possible to accelerate an object with mass infinitely quickly with nothing but an electric field? Sounds impossible more than likely. I feel that an instantaneous acceleration can only be caused by an infinite amount of energy given.