EMRFD Message Archive 13973

Message Date From Subject
13973 2017-06-05 09:04:22 richard kappler Capacitance and inductance
Old dog, new ham, absolute n00b at electronics. Working my way through the emrfd reprint as well as a couple other texts.

In regards to capacitors and inductors:
I'm an old Navy steam engineer, so when (can't remember which text) explained capacitance and inductance as analogous to fluid thru piping, turbines and such, it finally made sense to me.

So now I have the mantra, capacitors resist change in voltage, inductors resist change in current. Okay, no problem, I was qualified EOOW at an early age, had to learn my electric/magnetic theory, I get it. Sort of.

Then I sits and thinks... Ohms law. If voltage and resistance in the circuit don't change, how can an inductor 'slow,' née change, current? Concurently, if current and resistance don't change, how can a capacitor resist change in voltage where Ohm says there ought not be any?

Are we changing the supplied current/potential which causes this? Surely it can't  be a steady state circuit... or am I missing some big picture?

73, Richard W2KAP 
13974 2017-06-05 09:57:47 Bill Carver Re: Capacitance and inductance
Ohms law relates current and voltage applied to resistors. And, as a separate issue, when you multiply the voltage times the current, getting watts, that watt is dissipated as heat.

Ideal Inductors and capacitors are lossless, and they do not convert electrical energy into heat, even though there is applied (AC) voltage and current. They STORE energy. And they can return that energy back to you at a later time. In a hydraulic sense: it takes energy for you you to pump water uphill through a hose to a capacitor....er, a tank. But the next day, you can connect a Pelton wheel and generator to that capacitor...ah, tank, and get that energy back. 'Course inductors and capacitors are not lossless, nor is the pump, Pelton wheel and generator so you can't get back 100%.

The capacitor/tank concept is fairly easy to understand. Inductors, which store and return energy from magnetic fields isn't quite so intuitive. Even trickier (but kinda cute) is "resonance" in an LC circuit, where energy is alternately stored in the coil current, then the capacitor voltage, back and forth at a frequency 2*pi*square root of L* C. Lots of math has been developed to "describe" exactly what happens to the voltage, current and stored energy in sinusoidal AC circuits, or time-varying arbitrary transients. In the olden days (not that long ago) a lot of time/energy was spent mastering that mathematics. It's still useful to know if you're an engineer, but the gruntwork is now performed almost effortlessly by programs like LTSPICE.

Bill W7AAZ

13975 2017-06-05 14:10:40 kerrypwr Re: Capacitance and inductance
There's an additional factor in AC/RF circuits; phase.  Phase comes into play when dealing with reactive, ie capacitive or inductive, circuits.

There's a lot of information on "power factor" available; try a search on that term.

Understanding the importance of phase is a great leap forward in understanding RF; my first "hands-on" experience (the kind that I respond to) was when I bought a HP8405A vector voltmeter; I had several "light-bulb moments" when using that.

Later builds of my N2PK VNA and my DG8SAQ VNWA brought further understanding; I knew nothing about phase when I started and I now know at least ten times as much as that.  :)

Kerry VK2TIL.
13977 2017-06-05 19:40:17 Andy Re: Capacitance and inductance
Then I sits and thinks... Ohms law. If voltage and resistance in the circuit don't change, how can an inductor 'slow,' née change, current? Concurently, if current and resistance don't change, how can a capacitor resist change in voltage where Ohm says there ought not be any?

I'm not sure if this is what you're asking, but ....

Both inductors and capacitors work the way they do, by storing energy temporarily.  Inductors store energy in the magnetic field,  Capacitors, in the electric field between the capacitor's plates.  Resistors don't store any energy.

When something (anything) in a circuit tries to change the current flowing through an inductor, the magnetic field must respond, by also changing.  As it does, the changing magnetic field. in turn, induces a new voltage across the inductor.  Almost like a battery, temporarily.  And that affects the rest of the circuit.

If the inductor's current tries to decrease, the inductor takes some of that stored energy in its magnetic field, and returns it to the rest of the circuit.  The act of doing that, giving some of that stored energy back to the rest of the circuit, opposes the change in current.  So, a balance exists (with no more energy either added to or removed from the magnetic field) only when the current through the inductor doesn't change.  Whenever the current does change, there has to be energy either added to, or removed from, the magnetic field, and that takes extra work -- which is how the inductor tries to slow down the change in current.

A similar argument can be made about capacitors.

In a steady-state circuit, nothing is changing.  So if we're talking about inductors (or capacitors) slowing the change in current (or voltage), then it's not steady-state.

Ohm's law itself doesn't really apply to (ideal) inductors and capacitors.  Ohm's law works for resistors.  I'm a little confused about how you brought Ohm's law into the question, but maybe that's just me.


13978 2017-06-05 22:48:43 n3go Re: Capacitance and inductance

Hi Richard;

Let me first say that nobody is going to break Ohms Law anytime soon. :-) It works just fine with capacitance and Inductance. The missing piece being hinted at is called reactance. Reactance equates precisely to resistance; but at a specific frequency, at which point Ohms Law can be applied. Since the behavior of resistors is unaltered by frequency their opposition to current flow is constant and referred to as pure or real resistance. Both are measured in ohms to quantify their opposition to current flow.

    Inductive reactance (X sub L) is computed as 2 times Pi times Frequency in Hertz, times Inductance in Henries :   Xl = 2 * Pi * F * L

    Capacitive reactance (X sub C) is computed as the reciprocal of 2 times Pi times Frequency in Hertz times Capacitance in Farads  : Xc = 1 / (2 * Pi * F * C)

Reactance varies also with time (the reciprocal of frequency), and this variance is quantified in degrees of  rotation of a cycle. This angular measurement is called phase. Phase has relevance when combining R's, L's, and C's, which create a rotating vector with a magnitude which is then called Impedance. Impedance is also expressed in Ohms, and Ohms Law can be applied when all of the resistance and reactance values are known at a precise moment in time with respect to a specified frequency. This is where all the mathematics can get a tad challenging. :-)

   Slightly different than resistors though, reactances of Inductors and capacitors have the property that they cancel one another. This simply means that a capacitive reactance of 10 ohms reduces an effective 8 ohms of inductive reactance to a mere 2 ohms of net capacitive reactance. In a circuit with R's, L's, and C's, nothing is altered to the magnitude of the resistance... and of course, everything changes at the next moment later in time. By convention, Xc is expressed as a negative value which allows the reactances to be added together algebraically, as is done when adding resistors. Using this convention allows the result to always be positive if inductive and negative if capacitive.   

    Finally; we end up with a resistance of R ohms, and a net reactance of +/- X ohms. These are then added vectorially (using the Pythagorean theorem) to yield an Impedance of Z ohms:   Z = sqrt( R2 + X2)

    If we do our math right, we don't break Ohms Law, and no tickets are issued. :-)

    I might add that in most cases, the mathematics need not become any more cumbersome than given here, if an analysis is sufficient for a few spot frequency points. It only gets daunting when one wishes to compute the response over many frequencies, to observe phase response, to show waveform shape variations, or analyze transient behavior. Tools like LTSPICE are indeed the only way to approach this type of analysis. Such are the tools of an engineer.

      Also; the use of radian frequency to compute reactances, is the magic that allows us to keep the math simple and treat inductors and capacitors as though they were resistors when computing circuit values for a design. It also serves to simplify scaling known working circuits to other frequencies or different impedance environments. Ohms Law is our friend... we should not try to disobey. LOL!                
--  72  Gary, N3GO
13981 2017-06-06 22:20:56 Brooke Clarke Re: Capacitance and inductance
Hi Richard:

You are mixing up DC and AC. Ohms Law applies to DC circuits, but capacitors and inductors are used in AC circuits.

Have Fun,

Brooke Clarke, N6GCE

-------- Original Message --------
> Capacitance and inductance
13982 2017-06-07 03:50:14 Bob Re: Capacitance and inductance
There is a "secret path" to discover regarding Ohm's law in capacitance and inductance.  Unfortunately, it requires a bit of trigonometry and (ideally) imaginary numbers and complex numbers.

If you are familiar with imaginary numbers, there is a bit of confusion in electronics vs the rest of the civilized world regarding the figure used to show imaginary numbers:

Generally i (lower case i) is used to denote the "imaginary" square root of -1.  In electronics they often use j (lower case j) to mean the same thing.  In other words:

i = j = square root -1.

I hope I haven't scared you away with talk of trigonometry, imaginary numbers and complex numbers but they are not terribly hard to understand. Despite the name, they are not as complex as the term "complex number implies.

If you know about complex numbers I suggest you read (you can skim it to get the gist):


The pictures (graphs) can help a lot!

To learn about complex numbers, a tutorial here should help:


Good luck!

Feel free to contact me if you need more help on the topic.

13983 2017-06-07 07:43:02 Clark Martin Re: Capacitance and inductance
Ohms law still applies in AC as reactance and complex impedance.

Sent from an iPhone, don't ask whose.

13993 2017-06-10 21:28:52 Andy Re: Capacitance and inductance
  "Ohms law still applies in AC as reactance and complex impedance."

There is some debate about that.  If I remember my schooling correctly, **technically** Ohm's Law applies only to DC circuits and only to resistance.

But there is a logical extension to Ohm's Law that applies to AC circuits too, as long as you use the correct (complex) math, and only when you know that there is a frequency, that you keep track of.

The other important thing to remember, is that there's a huge difference between thinking about AC circuits, where a frequency is involved (and we talk about Z(f)) -- versus time-varying circuits, where we don't care about what the frequency is (or even if there is one) but instead we keep track of v(t) and i(t).

When we say that an inductor resists the change in current, or a capacitor resists the change in voltage, we are ONLY talking about the v(t) and i(t) time-domain representation.  The idea that a capacitor resists changes in voltage, doesn't really work (i.e., does not apply to the formulas) in the frequency domain where you are analyzing capacitors as having a reactance (or impedance) at a frequency f.

Likewise, using the AC extension to Ohm's Law does not work when we are looking at v(t) and i(t) with no knowledge of what the frequency is, or even if there is a frequency present.

Yes, the two are linked, of course.  But you have to be careful to keep the analyses distinct from one another.


13994 2017-06-11 06:02:07 Nick Kennedy Re: Capacitance and inductance

​That's very much the response I was wanting to give. I think the formula stating that current equals voltage divided by reactance (or impedance) is analogous to Ohm's law, but it's not actually that law. 

Maybe the distinction is a little fussy, but we get that way with technical stuff, don't we?


Nick, WA5BDU

13995 2017-06-11 09:39:00 Eamon Egan Re: Capacitance and inductance
To summarize and correct a few points

1. Impedance, the complex quantity, is expressed as: Z = R + jX

2. It was stated that impedance Z = sqrt(R^2 + X^2). In fact, this is true for  _magnitude of_ impedance