# Why capacitors and inductors affect the phase and resistors

hello!

why capacitors and inductors affect the phase of both current and voltage of a AC circuit and resistors don't?

let's say we have an AC circuit with resistors only, then there is no change in the voltage and current as imposed from the voltage/current source, right?

but what happens when we add a capacitor or inductor? why phase changes? and why voltage phase change and/or current phase change? and we mean change, in comparison to what exactly?

please elaborate in simple terms! you may use a mechanical analogue or something!

thanks!

## Answers and Replies

phinds
Science Advisor
Gold Member
2019 Award
Capacitors strongly resist voltage changes and inductors strongly resist current changes. They are active components compared to resistors which can handle instantaneous changes in voltage/current. You need to study the math of how these elements work.

Capacitors strongly resist voltage changes and inductors strongly resist current changes. They are active components compared to resistors which can handle instantaneous changes in voltage/current. You need to study the math of how these elements work.

I know the maths, I need to know the physical mechanism behind it

phinds
Science Advisor
Gold Member
2019 Award
I know the maths, I need to know the physical mechanism behind it
I guess I don't understand your question. The math describes the physical mechanism. The phase changes fall out directly from the math.

what I understand so far:

resistors oppose the flow of current and lower the voltage, as energy is being consumed into heat
but they don't resist to the change of current or voltage as imposed by the source

for some reason that I want to know, capacitors and inductors, resist (react? impede?) the change of voltage (and current?) because there is some electrical inertia involved
as they store voltage (and current) they act as a temporary source, which is a bit out of phase with the original source
combined together, these two "sources" make the whole voltage and current of the circuit to have a different phase (and value?) of the one of the original source

this is my understanding so far, I don't know if it's correct!

the root of that 'inertia' seems to be the built up charge in the capacitor (and the built up magnetic field in the inductor?)
it's really complicate to imagine how this actually work in every of the different phases (not phases like phi, but phases like different time periods) of the AC
in the beginning, the AC voltage starts from zero and increases, this makes the voltage of the capacitor to built up and increase (with a phase difference? if yes, why?)
then, how the capacitor's charge react to the decreasing increase of AC, to its plateau, to its decreasing, to its zeroing, to its inversion of its polarity, etc

anyone can relate to what I am talking about? anyone thought of these too?

phinds
Science Advisor
Gold Member
2019 Award
what I understand so far:

resistors oppose the flow of current and lower the voltage, as energy is being consumed into heat
but they don't resist to the change of current or voltage as imposed by the source

for some reason that I want to know, capacitors and inductors, resist (react? impede?) the change of voltage (and current?) because there is some electrical inertia involved
as they store voltage (and current) they act as a temporary source, which is a bit out of phase with the original source
combined together, these two "sources" make the whole voltage and current of the circuit to have a different phase (and value?) of the one of the original source

this is my understanding so far, I don't know if it's correct!
I'd say that's an excellent understanding.

phinds
Science Advisor
Gold Member
2019 Award
the root of that 'inertia' seems to be the built up charge in the capacitor (and the built up magnetic field in the inductor?)
it's really complicate to imagine how this actually work in every of the different phases (not phases like phi, but phases like different time periods) of the AC
in the beginning, the AC voltage starts from zero and increases, this makes the voltage of the capacitor to built up and increase (with a phase difference? if yes, why?)
then, how the capacitor's charge react to the decreasing increase of AC, to its plateau, to its decreasing, to its zeroing, to its inversion of its polarity, etc
I don't think that's quite the best way to look at it (although I may be misunderstanding your view) because it is not the "build up" of charge/current that is the issue it is the resistance to any CHANGE in the charge/current. This is beginning to sound circular because one way to interpret what I am saying is "the resistance to change happens because of the resistance to change", which is not helpful, but I can't think of a good way to express it. Do you see what I'm getting at, though?

Drakkith
Staff Emeritus
Science Advisor
If you understand what capacitance and inductance are, you should understand why capacitors and inductors resist changes in voltage and current. Do you know what those two terms mean and how capacitors and inductors work?

phinds
Science Advisor
Gold Member
2019 Award
If you understand what capacitance and inductance are, you should understand why capacitors and inductors resist changes in voltage and current.

Right. That's another way of saying what I said in post #4

Physior, in some ways your question sounds like "I don't understand inductors and capacitors but I want to understand why they do what they do". It is inherent in the understanding of these element to understand why they do what they do. The math describes it.

If you understand what capacitance and inductance are, you should understand why capacitors and inductors resist changes in voltage and current. Do you know what those two terms mean and how capacitors and inductors work?

I know capacitance only as an equation of area of plates, distance between them, etc
I know that capacitors store charge in their plates when we put them in a circuit

Drakkith
Staff Emeritus
Science Advisor
I know capacitance only as an equation of area of plates, distance between them, etc
I know that capacitors store charge in their plates when we put them in a circuit

Then I suggest reading more on capacitance, along with inductance if you know little about it.

Then I suggest reading more on capacitance, along with inductance if you know little about it.
but I don't have any question about capacitance or how capacitors work on DC
Capacitance is the ability of a body to store an electrical charge.
This is something easy to understand, and don't know how this relates to my question

Doug Huffman
Gold Member
• abecedarian
Drakkith
Staff Emeritus
Science Advisor
but I don't have any question about capacitance or how capacitors work on DC
Capacitance is the ability of a body to store an electrical charge.
This is something easy to understand, and don't know how this relates to my question

If that's all you know, then you've got a lot to learn. Specifically you need to learn how capacitance and inductance work together to give electrical reactance, which is the opposition to a change in either voltage or current: http://en.wikipedia.org/wiki/Electrical_reactance

Note that inductors and capacitors work differently in AC circuits than they do in DC circuits. Or, rather, that a DC circuit is a special case of an AC circuit where the frequency is effectively zero, so you don't see most of the effects you usually see in an average AC circuit.

Look at the wiki article I linked and hit up google. There should be plenty of articles online that explain electrical reactance, capacitance, and inductance. I'm about to head to bed otherwise I'd elaborate a bit more on the topic.

• abecedarian and Doug Huffman
I find many mathematical manipulations in these articles and not a simple understanding
can't you explain as nicely I did in my number 5 post?
I gave a good explanation, not sure if it is correct, but can be understood by anyone, without using maths

understanding the maths is not always the case
I can understand algebraic manipulations, but I need to understand the physical mechanisms behind them

phinds
Science Advisor
Gold Member
2019 Award
I find many mathematical manipulations in these articles and not a simple understanding
can't you explain as nicely I did in my number 5 post?
I gave a good explanation, not sure if it is correct
So did you not read my post #8?

• physior
Doug Huffman
Gold Member
Imagine this sort of dialogue about quantum theory and relativity.

IMO -- Resistors CONVERT energy from Electrical to Heat - it is then lost from the circuit ( Real POWER)... however Inductors and Capacitors (ideally) only STORE energy (granted the do convert to M and E field rep) - in an AC system they store and return energy in every cycle ( 50 / 60 times a second) .... this is referred to as imaginary power - because you have current and voltage - but you are not loosing any energy.
As for the change - we refers to the Phase angle of the current - relative to the voltage.

The phase shift is actually a bit of a special case for AC voltages/currents. The *actual* formulas for capacitors and inductors that relate the voltages to the currents involve a simple derivative (for the capacitor) or integral (for the inductor). It just happens to be that the derivative of a sine wave is the cosine wave, which is nothing but a 90 degree phase shift. The integral of a sine wave is a negative cosine wave, which is yet another 90 degree phase shift, but the other direction.

EDIT:
Capacitor formula: Inductor formula: (obviously the inductor formula becomes an integral when you solve it for 'i')

Last edited:
anorlunda
Staff Emeritus
As others said, capacitors resist the CHANGE in voltage, and indictors resist the CHANGE in current. In AC analysis, resistance to CHANGE is the same as a phase shift of 90 degrees.

Is that what you were asking about?

Doug Huffman
Gold Member
What about it? Do you even know the numerous books that explain them in simple words without mathematics and previous knowledge? Don't play the smartas
No, which ones are these, "numerous books that explain them [quantum theory and relativity] in simple words without mathematics and previous knowledge?"

Doug Huffman
Gold Member
The first link in google mentions many books:
http://www.perkel.com/nerd/relativity.htm don't be that lazy Especially when you play the smartas
Well, to begin with, I do not use G00gle. Second, I have a fine collection of original source materials. Perhaps preeminent among them is a xerox copy of Stephen Hawking's BLACK HOLES AREN'T BLACK in typescript with manuscript special characters and drawings (part of my collection of Gravity Research Foundation prize winning essays). Another from my classroom days is Samuel Glasstone's The Sourcebook on Atomic Energy (Krieger 1979).