Impedance

[alondouek]

Can somebody please explain the concept of impedance?

Thanks

[appianway]

Is this for circuits? Think of it as a complex resistance of sorts - it's basically just like another form of resistance.

[alondouek]

I came across it while researching the effect of demyelination on neuronal signal transmission. The particular equation I came across was , which I think (but actually have no idea) is analogous to ohm's law? Subscript m simply denotes 'membrane'.

I asked one of the bioelectricity lecturers about this equation, and the only thing he was able to tell me was that the second term was impedance. I still have no idea what it is, but then again most physics goes over my head...

How does it differ from regular resistance? There's clearly a difference as per the above equation, but what that difference is eludes me.

[appianway]

This is where things become a bit different. When you're dealing with circuits, complex numbers are the most natural numbers to use (especially for sinusoidal signals). Basically, you can think of impedance as the complex component of resistance - it's something that comes in when you have capacitors (which store charge/voltage) and/or inductors (which store current). If you want a less qualitative description, wikipedia has a decent explanation of it here: http://en.wikipedia.org/wiki/Electrical_impedance#Deriving_the_device-specific_impedances

Basically, resistance as you know it is still part of the resistance. However, now you have another component!

[alondouek]

Thanks for the reply! Just a couple more questions (keep in mind that I'd not done any physics up until 11 weeks ago, in case these questions are particularly dumb):

• Why do we use complex numbers in circuitry? Does it have anything to do with the time constant, ?
• In neurons, alternating current is present, but why is this? Nervous signals only travel in one direction along the neuronal axon, so wouldn't DC be more appropriate in this scenario?

I really appreciate the qualitative answers; my biophysics unit is being taught with the least possible amount of mathematics involved.

[appianway]

We use complex numbers in circuitry because it turns out that AC signals are sinusoidal, so we can write them of cos of some stuff. However, there's this nice relation that says that e^(ix) = cos(x) + isin(x), so if we take this exponential form and say that we only care about the real component, we can write everything in terms of e^(ix) instead of cos(x). That's how to get complex numbers starting to come up everywhere.

I can't answer the question about the neurons - I've done no biology ever basically..

[alondouek]

Thanks again.

With the sinusoidal nature of the AC signal, which parts are real and which parts are complex? Also, why is this - effectively, why can't we express everything in these signals with real numbers?

I was doing a bit of thinking today about impedance (it's not even relevant to my studies, I just can't get the concept out of my head), and I arrived at the notion that if capacitance is a factor in a circuit, then voltage and current would have to flow at different rates in AC as one would lag the other. Is any of this actually valid or useful? Does it have any relation to the use of complex numbers in circuitry? I have no idea what I'm doing

[appianway]

The real part of the signal is what you see - it's the part that matters. The complex part arises from the notation - it's much easier to deal with exponentials than complicated sinusoidal functions.

It's great that you're thinking about this! Mega respect. And your intuition is spot on - it creates a phase difference between current and voltage which appears in the complex exponent.

[alondouek]

So is this phase shift impedance? I mean, if impedance can be shown as , I guess this makes sense, if ω is frequency, C is capacitance and j is the complex number - then the 'lag/lead' relationship can be shown by the above term by equating it to V, right? Wouldn't that mean that the impedance of a capacitor can only be complex?

Anyway, I should stop procrastinating Thanks for all your help, it has really cleared things up!