# AC square wave currents across resistor (no capacitor, no inductor) and gravity air resistance analogy

Update edit: my question is really does alternating electric current through a simple resistor have a mass-based inertia that introduces lag if the frequency of oscillation is high enough? Are there every situations where inertial lag would be relevant? I'm not asking about parasitic inductance of real materials.

I have a question about whether an analogy exists or doesn't exist between: 1) a circuit with alternating square wave voltage source and a resistor (no capacitor, no inductor) 2) a ball thrown upwards into the air against gravity with drag My question is whether a transient slosh or lag of the current across a resistor (no C, no L) is known to occur. I started thinking about this because air resistance and RC circuits are both described by similar first order diff eq. But Ohm's law imposes a constraint on initial conditions for the circuit that doesn't exist for the ball, that current across a resistor always moves from high to low voltage.

To conceptualize the current in the resistor, I'm imagining removing the capacitor and considering an AC circuit with only a power source and a resistor (no C, no L). The textbook I'm reading (Halliday & Resnick) shows that current and voltage stay in phase for a sinusoidal AC in this circuit. This seems to follow from Ohm's law in DC circuits, where current is defined to move from high to low voltage. It seems to me that Ohm's law prevents an initial condition where the current moves against its voltage gradient, in contrast to the analogy of throwing a ball up into the air.

I understand that the change in electric field and electrostatic potential transmits very rapidly (nearly speed of light) through the circuit, but it seems like the charged particles have still acquired a momentum that takes a certain amount of time to change. Is such a lag measurable in some simple AC R circuits, perhaps very high frequency square waves? Perhaps also high amplitude square wave? I don't know how it would be measured. I don't know if this would mean charge accumulation in some part of the circuit. Oscilloscopes measure voltage, and I'm trying to imagine the current. I also know that if the current was measured by introducing a capacitor, this would introduce a phase change between voltage and current from the capacitor. My question is about isolating any phase change contribution from the resistor itself. I imagine that this would be equivalent to asking if the impedance of a resistor is truly frequency and amplitude independent. I know this isn't the way that the introductory textbooks are presenting circuits, but I'm curious if this is a known real-world phenomena in some cases, perhaps in device physics?

• I think you need to consider that there is a resistance to current change (inductance) and might be low, but never zero in any real material. – BowlOfRed May 9 '18 at 17:01
• -1 Not clear what you are asking. Are you asking if real resistors can have capacitance or inductance? If so, your question is a possible duplicate of Electric field and capacitance across a resistor – sammy gerbil May 9 '18 at 18:10
• After reading about parasitic inductance, I think I'm really asking about whether electrical current has a mass inertia that introduces a lag when the voltage is switched. It looks like parasitic inductance can introduce a lag. I know that the masses of charges are small, but I'm curious if the frequency of oscillation is high enough, does this introduce a lag. I'm not certain, but my intuition is that this is different than the material property of inductance in real resistors. – lamplamp May 9 '18 at 18:44
• I'm not quite sure what you're looking for but physical resistors have both a parasitic inductance and capacitance and, thus, a resonance frequency and a Q that, for example, RF engineers and RF simulation software account for with a high-frequency model of a resistor. In other words, physical resistors have a frequency response – Alfred Centauri May 9 '18 at 21:53
• Thanks, I'm really asking does the Newtonian inertia from the tiny mass or momentum of the electric current become significant if the frequency is high enough. I know that there are other real material factors for intrinsic capacitance and inductance. – lamplamp May 9 '18 at 23:09