# How can current phase shift be 90 degrees behind voltage just "inside the capacitor" on an RC series circuit but be in phase in the resistor?

Imagine an AC source in series with an RC circuit.

In this video, the instructor claims current will be 90 degrees behind voltage inside the capacitor but not inside the resistor or the whole circuit. If that's true, I don't understand.

I am imagining current as a flow of water inside a tube and I cannot see how the water can be delayed on a point in the tube and not delayed 1 inch later.

• In a capacitor, the current leads the applied voltage by 90 degrees. Mar 3 at 16:20
• my mistake, sorry.
– Duck
Mar 3 at 21:18
• Duck, it's not your mistake. The guy in the video says current lags voltage by 90 and NO WAY does it do that in a million years. Mar 3 at 22:28
• I'm always a little curious as to who some of these self-styled experts are. However I think that the fact that Dave Jones (Eevblog) joins him in a different video youtube.com/watch?v=NnjJL6Uhock gives him a bit of credibility. Mar 5 at 14:44

He does say, at 13:12 "that 90° phase shift only happens in the capacitor", which is an unfortunate choice of words. The word "in" or "inside" might give the impression that current inside some component is different from the current outside it, which is false. In this simple loop, current passing all points, inside and outside of any component or wire is the same at any given instant in time.

I would phrase it using the words "across" and "through", as follows:

The voltage across the capacitor varies 90° out of phase with the current through it.

This is relating the voltage across the capacitor to the current through it. It is not a statement about current inside compared to current outside. It is not a statement about any voltage inside the capacitor compared to any voltage outside it. I repeat, this is a statement comparing how voltage across a capacitor varies in relation to the current through it. It's not a proportional relationship, like a resistor.

If you are mathematically inclined, such behaviour is described in this well established relationship:

$$I = C \frac{dV}{dt}$$

This is saying that current $$\I\$$ through a capacitor is proportional to the rate of change of voltage $$\V\$$ across it. Contrast that with the behaviour of a resistor:

The voltage across the resistor varies in phase (0° shift) with current through it. Ohm's law reflects this behaviour:

$$V = I \times R$$

That is saying that voltage $$\V\$$ across a resistor is always directly proportional to the current $$\I\$$ through it, and the constant of proportionality is resistance $$\R\$$. No mention here of "rate of change" of anything.

• ok I see. I was approaching this as voltage and current were two independent entities. There is no such thing as voltage for that matter. What is important is current, Current creates the voltage.
– Duck
Mar 3 at 21:17

The instructor does not say the current is different in the two components. He says the phase shift is only in the capacitor and he says the voltage and current are in phase in the resistor.

The current is the same through both components but the voltage across the two components is changing out of phase with each other.

... the instructor claims current will be 90 degrees behind voltage inside the capacitor but not inside the resistor

He's given the wrong polarity for current, and we need more precise words for 'inside', 'through' for current, and 'across' for voltage, and reject the possible implication that the voltages are in phase.

The current through a capacitor is 90 degrees ahead of the voltage across it

The current through a resistor is in phase with the voltage across it

When they are in a series circuit, their currents are necessarily in phase, it's the same current, and their voltages are out of phase by 90 degrees.

• Neil, it's plain wrong, the current leads the voltage. Mar 3 at 19:45
• @Andyaka what's the difference between '90 degrees ahead', and 'leads'? Mar 3 at 20:46
• The quote says 90 degrees behind so how might this be true? Mar 3 at 21:03
• @Andyaka Ah, you are quite right. The answer illustrated my regarding polarity as unimportant, too much working with IQ systems, too many things to swap. Just plug it in at the end, and see whether it's the right way round, and swap something if it isn't. The reason for the separate answer was to emphasise the fundamentals - currents in a series circuit are in phase, voltages are across and currents through, which in my view were more wrong than the actual polarity issue. However, good that you're keeping everyone's i's dotted and t's crossed. Mar 4 at 11:42

It must be wrong then. If you think that all Youtube videos must be correct then you should have some critique. Anyone can claim anything on the Internet and it might be false or incorrect.

Current flows in a loop and KCL says all current must always equal at all times through the loop. So resistor and capacitor currents are equal at all times.

And in a resistor, current directly defines the voltage, but in a capacitor, current directly defines the rate of voltage change.

Also current does not lag voltage in a capacitor. Current leads voltage in a capacitor.

• that's why I am here :D because you always have to believe it with a grain of salt,
– Duck
Mar 3 at 21:18

In you question you suggest the water flow metaphor - a question that has not been addressed by others. The water metaphor fails as explanation in this and some other aspects, I feel.

First, a bit off the topic, the current flow in a conductor is indeed in phase first with magnetism (always) and with the resistance - which involves Jule-an current "wasting" or "burning" and production of heat - the consumption of power.

Again, a bit of the topic (but quite analogously to some relations quoted by others0 you probably know that if the circuit has self induction e = L di/dt there is an induced back emf which lags behind current by 90 degrees - and according to Charles Steinmetz being an action/reaction phenomenon causes a wattless drop of potential (reactance component - which added in quadrature with resistance - by pythagorean theorem equals impedence).

Watless - in other words - means energy is used to build magnetic field and restored by collapse of the magnetic field that again induces current - all in the proper phase relation. Here inductance (L) a coefficient of energy storage by lines of magnetic force. It is actually quite analogous to "C" which is a coefficient of energy storage by static lines of force - at least it was described so by old 19th century electricians.

With the issue of the capacitor,inside it, as some other posts rightly indicate (there is a displacement "flux" established in the dielectric and as 19th century electricians knew it could be made "denser" with different dielectric permittivities). Nowadays we talk about charge on plates but Steinmetz complains about this thinking, in 19th century they thought that it was dielectric which was polarized (confirming the fact experimentally). SO.... If there were no inductance and/ or resistance in the entirety of the circuit at the moment of closing the switch the capacitor would have charge instantly. Remember the old experiments in electrostatics? - the condition of tension (difference of potential) influenced by bringing a charged ball to the insulated conductor and disappearing as it was withdrawn- if you were clever you could actually have a two part joint conductor and separate the minus and plus charges if you avoided discharging to ground). The "charge" induced by this (as they called) "influence" would be permanently left on both sides unless discharged to ground.

Quoting Steinmetz in the case of alternate current "current flows into the condenser during rising EMF and out of the condenser during decreasing EMF" that is current "consumed by the condenser leads the impressed EMF 90 degrees" - reference "Theoretical Elements of Electrical Engineering" by Charles Proteus Steinmetz page 56.

The following are copies of pages 17 and 18 from Theory and Calculation of Transient Electric Phenomenta by Steinmetz.

PS. For consistency, above Steinmetz does talk about charges on plates but in earlier publications he quietly complains, a lot of terms and ideas have changed since first publications within a decade or so .... (that's also confirmed by one Eric Dollard)

• brilliantly explained, thanks!
– Duck
Mar 4 at 23:50

The current through the (ideal) capacitor is a displacement current. The current through the resistor is a conduction current. They are different. The displacement current is associated with a time changing electric field inside the capacitor due to charge accumulation on the plates. Check out Maxwell's equations.