# No inductor - any induced EMF when switch flipped on?

My instructor put in the notes a picture of a loop without an inductor - just a battery with voltage $\epsilon$, a switch, and resistor with resistance $R$. He explains that as soon as the switch is flipped, an emf is created that will oppose the change in flux. With an inductor, I can see how this would happen. But this made me wonder what happens when there isn't an inductor. Does current immediately reach $\epsilon\ /\ R$? Or is there some back emf that opposes flux change? It would make sense thinking about it that even without an inductor, there would be a resistance to flux change inside the closed loop, so it wouldn't immediately reach $I = \epsilon\ /\ R$.

• A loop of wire is an inductor, it just doesn't usually have a particularly high inductance. Apr 19 '17 at 5:27

The answer to your question is that there is always inductive coupling between the legs of such a loop. Beyond that, transmission line theory answers your question of what happens. Basically, there's parasitic inductance and capacitance everywhere you go, and they ensure you never see instantaneous jumps in current.

• Thank you!! So does an inductor effectively just amplify this a ton by its solenoid shape? Apr 19 '17 at 4:14
• Yes. The shape of the inductor creates a stronger magnetic field than you'd get from stray wires (far stronger!). In fact, it's so much stronger that in most calculations you can ignore any magnetic effects that don't involve a bunch of loops of wire. Only at high frequencies and corner cases (like the one you mention) do we start having to pay attention to parasitic inductances. Apr 19 '17 at 4:18
• Interestingly enough, this is one of the first lessons in the definitive book on high speed digital electronics: The Art of High Speed Digital Design: a handbook of black magic. In it, they describe how a capacitor can start to look like an inductor at high frequencies because the capacitor's two metal legs start to create a noticeable inductive effect. Trimming the capacitor legs actually changes the character of the circuit! Apr 19 '17 at 4:20
• thank you Cort! Extremely informative! Would you be able to explain why the capacitor legs have a relatively large inductive effect? Apr 19 '17 at 4:22
• The legs are two parallel wires, and parallel wires couple inductively. It's not a lot of inductance, but at high frequencies (gigahertz), it doesn't take a lot of inductance to create a high impedence (resistance at a given frequency). And by "corner cases" I meant unusual circumstances like "I actually care about whether its an instantaneous rise or fall, or just a really really really fast one." Apr 19 '17 at 4:25