# Is capacitance more fundamental than resistance?

• Jirnyak
In summary, capacitance is more fundamental than resistance because there are no dissipation at the end in a whole system because it is electric field distribution around the space.f

#### Jirnyak

When we have electrical resistance it is based on dissipation of energy, when we have reactance it is a consequence of charge accumulation in capacitance. Together they form impedance. But let's consider what exactly is responsible for dissipation in case of resistance? Is not it because of interactions with small capacitances (because every area in space could have one)? Everything could have a capacitance even electron (is it true? It's area is 0 so it would be charge of electron divided by 0, that's could be treated as infinite capacitance), but it is non sense to speak about the resistance of electron (or is it?). So can one speculate based on these arguments that capacitance is more fundamental than resistance because there are no dissipation at the end in a whole system because it is electric field distribution around the space (so, no resistance)

Last edited:
• alan123hk and Delta2
Who is writing this post ? An Oxford graduate ?

At least clean your keyboard !

• • nasu, davenn, Vanadium 50 and 2 others
Who is writing this post ? An Oxford graduate ?

At least clean your keyboard !
Why do you think I am Oxford graduate?

conceequebce
What's a conceequebce?

I am also having trouble parsing your post. Did you dictate it on your smartphone and not proofread it? That's okay, but if you could clean it up a bit, that would make it easier for us to respond to the substance of your question. As it is now, I can't make heads nor tails of your question.

• Delta2 and Jirnyak
What's a conceequebce?

I am also having trouble parsing your post. Did you dictate it on your smartphone and not proofread it? That's okay, but if you could clean it up a bit, that would make it easier for us to respond to the substance of your question. As it is now, I can't make heads nor tails of your question.
Sorry and thank you.

• berkeman
Why do you think I am Oxford graduate?
Because you posted that
I am 25 and I have graduated from Oxford university in Chemical Biology but strongly believe that I want to do Physics all my future life. I did my Masters by research on the department of Chemistry and I was co-supervised by Professor in Organic Chemistry and Professor in Physical Chemistry. So that's why I fell in love into Physics. I was doing a lot of NMR and quantum mechanics and started to like Maths which I hated before.
...

Because you posted that
I forgot about that post. Pls no offtop.

offtop
What's an offtop?

But let's consider what exactly is responsible for dissipation in case of resistance?
Maybe I'm too simple minded, but I have absolutely no idea what you're trying to do. You can describe the dissipation of energy in a resistor by e.g. the Drude model. Take the mean 'lifetime' between collisions to be ##\tau##, and under the action of a general external force ##\vec{F}## the momentum of the electron is updated like$$\langle\vec{p}\rangle(t+\delta t) = P(\mathrm{not\, scattered})(\langle\vec{p}\rangle(t) + \vec{F} \delta t) + P(\text{scattered}) (\langle\vec{p}_{\text{random}}\rangle + \vec{F} \delta t)$$i.e. if the electron collides, then it's momentum immediately after the collision is randomised and in time ##\delta t## it picks up a further ##\vec{F} \delta t## worth of momentum. Since ##P(\mathrm{not\, scattered}) = 1- \frac{\delta t}{\tau}## and ##P(\mathrm{scattered}) = \frac{\delta t}{\tau}##, you have$$\langle\vec{p}\rangle(t+\delta t) =\langle\vec{p}\rangle(t) + \vec{F} \delta t - \frac{\delta t}{\tau} \langle\vec{p}\rangle(t) + \frac{\delta t}{\tau} \langle\vec{p}_{\text{random}}\rangle \implies \frac{d \langle \vec{p} \rangle}{dt} = \vec{F} - \frac{1}{\tau} \langle \vec{p} \rangle$$For something like a resistor you'll have an ##\vec{E}## field providing the external force ##\vec{F}##, so$$\frac{d \langle \vec{p} \rangle}{dt} = -e\vec{E} - \frac{1}{\tau} \langle \vec{p} \rangle \implies \frac{d \langle \vec{v} \rangle}{dt} = -\frac{e}{m_e}\vec{E} - \frac{1}{\tau} \langle \vec{v} \rangle$$In the steady state you just take the LHS to be zero and out comes $$\langle \vec{v} \rangle = - \frac{e\tau}{m_e} \vec{E} \implies \vec{J} = \rho\langle \vec{v} \rangle = \frac{ne^2\tau}{m_e} \vec{E} := \sigma \vec{E}$$Then, the power of the electric field per unit volume is just going to be$$\mathcal{P} = \sum_{i \in V} -e\vec{E} \cdot \vec{v}_i = -ne\vec{E} \cdot \langle \vec{v} \rangle = \sigma E^2$$and thus, e.g. in the case of a simple cuboidal resistor with dimensions ##A \times L##, $$P = \int_V \mathcal{P} dV = \int_V \sigma E^2 dV = \sigma E^2 AL = IV$$where we used that ##EL = V## and ##\sigma E = J##. But in the steady state, the electrons don't leave the resistor with any net gain of kinetic energy, so this energy must ultimately be transferred to the resistor [e.g. thermal energy in the metal ions].

Last edited by a moderator:
• vanhees71, sysprog and Delta2
When we have electrical resistance it is based on dissipation of energy, when we have reactance it is a consequence of charge accumulation in capacitance. Together they form impedance.

No, you also have inductive reactance in many cases, not just capacitative reactance, i.e. ##X = \omega L - \frac{1}{\omega C}##.

Dissipation for a resistor is a cooperative effect. It is historically the seminal example of the fluctuation-dissipation theorem. It is not a time reversible component
Therefore it is akin to the viscous drag and not really a fundamental electromagnetic quantity at all.

• • vanhees71, berkeman and etotheipi
Summary:: Is capacitance of electron infinite?

Everything could have a capacitance even electron
Well I doubt seriously about this. Usually the capacitance is defined for some sort of structure where the electric charge can be varied (by charging or discharging). But the electric charge of electron is constant, we can't charge or discharge an electron, so i seriously doubt , even if we can define capacitance for an electron, we wouldn't find any use for this capacitance.
And the capacitance of electron might not be infinite (not sure about this at all). According to some model, we can model the electron as a small sphere with non zero radius .

Last edited:
• etotheipi
Summary:: Is capacitance of electron infinite?

When we have electrical resistance it is based on dissipation of energy, when we have reactance it is a consequence of charge accumulation in capacitance. Together they form impedance. But let's consider what exactly is responsible for dissipation in case of resistance? Is not it because of interactions with small capacitances (because every area in space could have one)? Everything could have a capacitance even electron (is it true? It's area is 0 so it would be charge of electron divided by 0, that's could be treated as infinite capacitance), but it is non sense to speak about the resistance of electron (or is it?). So can one speculate based on these arguments that capacitance is more fundamental than resistance because there are no dissipation at the end in a whole system because it is electric field distribution around the space (so, no resistance)

I think I can roughly understand what you mean. Although I am not capable of answering your questions, I can fully feel your pursuit, curiosity and enthusiasm for physics and natural science. • Delta2
And the capacitance of electron might not be infinite (not sure about this at all). According to some model, we can model the electron as a small sphere with non zero radius .

There is a way to do it using the classical electron radius. The capacitance of a a spherical capacitor consisting of concentric shells of radii a and b (b > a) is $$C=\dfrac{4\pi\epsilon_0}{\dfrac{1}{a}−\dfrac{1}{b}}.$$ Now let b→∞ and with the classical electron radius ##a=\dfrac{1}{4\pi\epsilon_0}\dfrac{e^2}{mc^2}##, you get ##C_e=\dfrac{e^2}{mc^2}.## However, I wouldn't know how that applies to what OP is trying to do because I don't know what
interactions with small capacitances

• Delta2
because I don't know what
I also had trouble understanding part of the post, especially this part ...

• kuruman
But let's consider what exactly is responsible for dissipation in case of resistance? Is not it because of interactions with small capacitances (because every area in space could have one)?
What does this even mean? Resistance arises from the collision of electrons, as pointed out above, with impurities and defects in the host crystal and with phonons.

• vanhees71
I find your concept of resistance too confusing to comment on. Anyway others have covered that pretty well.

However, I do agree in a rather pedantic way that capacitance and inductance could (sort of) be considered "more fundamental" than resistance. Resistance is a property of materials, and if you manage things right you can have 0 resistance. Capacitance and inductance are fundamental to charged particles and the fields they create. If you have a charged particles moving you can not avoid some inductance and capacitance.

Still it seems rather pointless, IMO. I think they are all fundamental enough.