What capacitors and inductors do

[Richardcavell]

I have learned that capacitors and inductors can be used for the following:

1. Separating AC from DC
2. Separating low frequency and high frequency AC
3. Phase shifting

But it seems to me that capacitors and inductors will always do these things. Is it the case that a designer of a circuit will choose a cap or inductor for just one of these reasons, but they will do the others anyway? How do you eliminate the unwanted features of a cap or inductor?

[PGPG]

Capacitor function depends on what it was used for by designer.

Knife can be used to cut bread or cat a rope. If you use it to cut bread you need not to do special actions to eliminate its possibility to be used to cut a rope.

[SteveThackery]

I have learned that capacitors and inductors can be used for the following:

1. Separating AC from DC
2. Separating low frequency and high frequency AC
3. Phase shifting

That is misleading, not least because it implies that it's a complete list.  Those are all "second order" effects; they are applications of capacitors and inductors, they aren't what capacitors and inductors actually "do".

Capacitors and inductors have electrical characteristics which are described by mathematics and the laws of physics. These characteristics enable - usually in combination with other components - many useful functions: decoupling, filtering, DC blocking, etc, just like your list.

To answer your question: "careful design" is how unwanted behaviours are rendered unimportant or irrelevant.  For example, you might want a DC block. Unfortunately, DC blocks can also attenuate low frequency AC. So its up to the designer to specify a capacitor large enough that any attenuation is too little to worry about.  That is how you choose which characteristics play a role, and which don't. Sometimes it isn't even possible to avoid side effects. For example, in most filters, the frequency-cutting function comes with phase-shifting, whether you want that or not.

[Terry Bites]

What they do is store energy, and out of that comes a miriad of circuit applications.
Capacitors store energy as electric charge and inductors store energy in a magnetic field.

[TimFox]

Another elementary detail about capacitors and inductors:
You cannot change the voltage across a capacitor instantaneously.
You cannot change the current through an inductor instantaneously.
For the capacitor, that would require an infinite current.
For the inductor, that would require an infinite voltage.

Real equations:  for capacitor, Q = CV, therefore I = C dV/dt
Similarly, for inductor  V = -L dI/dt
Polarities for voltage and current are left as an exercise for the reader.

[Konkedout]

Building on the post by TimFox:

I am an engineer who is not the best at calculus.  But you will do yourself a favor if you understand...a bit of differential calculus to begin with.

Understand that the current in a capacitor is the capacitance (in farads) * the rate of change of the voltage across it in volts per second.

Similarly, the voltage across an inductor is the inductance (in henries) * the rate of change of the current through it in amps per second.

Now we more commonly work with microfarads, microhenries, and faster changes in current and voltage.  But a calculator will take care of that so long as you are careful with your decimals, zeroes, or engineering notation (my preference.)

I feel certain that understanding these relationships is essential, and may get you to an "Aha! Moment."

[golden_labels]

What capacitors do. In many of those applications inductors are working together with capacitors.

Individual inductors are capacitors’ duals, so some things may be implemented with either. Capacitors usually take precedence due to smaller size and cost, or because inductors’ operation requires signals in current.

Inductors become more interesting, when they’re coupled (e.g. in a transformer).

Note that your point #2 already includes #1.

[PGPG]

Real equations:  for capacitor, Q = CV, therefore I = C dV/dt
Similarly, for inductor  V = -L dI/dt

I had it 40 years ago.
When we use typical voltage current directions (voltage arrow points to top (1) pin, while current arrow goes from top (1) pin through element (C or L)) then for C positive current makes voltage rising so no '-' needed and for L positive voltage makes (such directed) current to rise so I don't know where from '-' here. But I know it happens to see '-' in this equation.

[PGPG]

But you will do yourself a favor if you understand...a bit of differential calculus to begin with.

I 100% agree with that.
I just planned to write something like "If you seriously plan to play with electronic don't neglect math, ever!" but found it was already written.

To Richardcavell:
We don't know what is your math level but it looks being probable that you never seen something like dV/dt. Because of this few sentences from me.
t0 - a time moment we start analyse what is going on.
t1 - a time moment little later.
Δt=t1-t0 - the time interval that elapsed between t0 and t1.
V0 - voltage (at capacitor) in the t0 moment.
V1 - voltage in the t1 moment.
ΔV = V1-V0 - voltage change during Δt.
ΔV/Δt - speed of voltage change - how fast it changes.
For capacitor you can write: I=C * ΔV/Δt.
Example: C=1000uF, ΔV=-1V, Δt=10ms. With this values we get I=1000u * (-1)/10m = 1m * (-1)/10m = -0.1A.
So if after bridge rectified 50Hz voltage you use 1000uF capacitor than if you will be taking (taking out capacitor means it is negative current for it) 0.1A from it than between pulses charging capacitor (they are 100Hz - so once per 10ms) the voltage at capacitor will drop 1V (voltage change -1V = 1V voltage drop).
This calculation is true, but it is provided I is constant. In real life I is not constant, but in many cases we (using engineering approach) can assume I is 'enough constant to ignore its changes'.
If you need exact calculations (when current also varies) you assume that you change your analyse into lot of very, very short time periods being so short that you can assume I is constant during each such going to 0 time period. In math representation you replace Δ with d. This d means it is Δ but with assumption that it is going to be shorted and shorted until it is almost 0.
So equation I=C * ΔV/Δt changes into I=C * dV/dt. There are math methods (differentiation and integration) that allow you to find V as a function of time if you know I as a function of time and vice versa. Even when you don't know anyone of them but from other elements around capacitor you can find the other relation between I and V than you can find both these functions.
The simplest example of such case is capacitor charged to some voltage and connected paralel with resistor. From voltage and R you have current so you can calculate how voltage drops at C, but when voltage drop a little than current changes (because Ohms law) so the speed voltage is dropping down also changes and so on into infinity. Let us stop at the information that from both relations (one for R and second for C) you can find voltage and current for any time moment. When you will be taught at math about 'e' constant remind this what I have written here.

[TimFox]

Two more elementary observations about capacitors and inductors in AC circuit applications, where the voltage and current are stable sinusoids:
As a function of frequency, the reactance (imaginary component of impedance) of a capacitor decreases with frequency, and that of an inductor increases with frequency.
If you put a capacitor and inductor in series, there exists a frequency where the two reactances (of opposite sign) cancel leaving zero net reactance (series resonance).