# What is Capacitance: Definition and 899 Discussions

Capacitance is the ratio of the amount of electric charge stored on a conductor to a difference in electric potential. There are two closely related notions of capacitance: self capacitance and mutual capacitance. Any object that can be electrically charged exhibits self capacitance. In this case the electric potential difference is measured between the object and ground. A material with a large self capacitance holds more electric charge at a given potential difference than one with low capacitance. The notion of mutual capacitance is particularly important for understanding the operations of the capacitor, one of the three elementary linear electronic components (along with resistors and inductors). In a typical capacitor, two conductors are used to separate electric charge, with one conductor being positively charged and the other negatively charged, but the system having a total charge of zero. The ratio in this case is the magnitude of the electric charge on either conductor and the potential difference is that measured between the two conductors.
The capacitance is a function only of the geometry of the design (e.g. area of the plates and the distance between them) and the permittivity of the dielectric material between the plates of the capacitor. For many dielectric materials, the permittivity and thus the capacitance, is independent of the potential difference between the conductors and the total charge on them.
The SI unit of capacitance is the farad (symbol: F), named after the English physicist Michael Faraday. A 1 farad capacitor, when charged with 1 coulomb of electrical charge, has a potential difference of 1 volt between its plates. The reciprocal of capacitance is called elastance.

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1. ### Capacitance of three concentric shells

I want to calculate the capacitance of this system between the points x&y. So suppose I give a charge Q to the outermost shell and -Q to the innermost shell. To find the capacitance C, I try to find the potential V between the outermost shell and innermost shell . To find V ,I integrate the...
2. ### B What is the capacitance between two points on three concentric shells?

A friend of mine sent me this problem about finding the capacitance. We have three concentric shells of radius a, b, c. And we've to find the capacitance between x and y. I need help. Thank you
3. ### B Why can't we calculate capacitive reactance like u/i?

When I write ##X_C=\frac ui=\frac{U_\mathrm m \sin \omega t}{I_\mathrm m \sin \left(\omega t+\frac{\pi}{2}\right)}##, it should be ##\frac{U_\mathrm m}{I_\mathrm m}##, but it isn't. Why?
4. ### Why Capacitors in Parallels vs. Series: Coaxial Capacitor Case

So my idea was to separate the capacitor into two individual ones, one of length ##l - a## filled with a vacuum and one of length ##a## filled with the glass tube. The capacitances then are $$C_0 = \frac{2 \pi \varepsilon_0 (l-a)}{\displaystyle \ln\left( \frac{r_2}{r_1} \right)}$$ for the...
5. ### Equivalent capacitance of a circuit

Why is it that, due to symmetry, ∆V2 = 0 and ∆V1 = ∆V4 = ∆V5 = ∆V3? I don't really understand the reasoning behind the simplification. Thank you.
6. ### Change in energy stored in a spherical Capacitor

I have attached my solution. Unfortunately, after plugging in the values, my answer is 4 times more than the expected one. What am I missing?
7. ### Finding possible combinations of capacitors given circuit capacitance

For this problem, The solution is, Is the only way of finding the possible combinations is by drawing out circuit diagrams? Many thanks!
8. ### Capacitance of a parallel plate capacitor with a metal plate kept inside

Because of the plate P, the capacitor becomes a piece of conductor. It contains zero net charge and has 0 potential difference. Hence, the capacitance is ## \frac 0 0 # # that is undefined. The capacitance of a capacitor is defined as its capacity to store charge when a potential difference is...
9. ### Derivation for capacitance of cylindrical capacitor

I don't understand how they got from the previous step to the next step of the derivation circled in red: Many thanks!
10. ### Finding equivalent capacitance

There are 3 parallel paths: one through 4.0 µF, one through 6.0 µF, and one through 5.0 µF and 7.0 µF. Why wouldn't there be another path through 4.0 µF, 7.0 µF, 5.0 µF, and 6.0 µF? Also, what determines the direction of current flow when there is a diagonal across parallel paths? Thank you.
11. ### RC Circuits: Measuring Capacitance

I thought that if the slope of the T versus R graph is 4.00μF, then the capacitance would be 4.00μF but it says that's wrong. I know I'm doing something wrong but I'm not sure how to approach this problem. Can someone help?
12. ### Find the Capacitance based on 3 different switch positions

You can find the impedance for each of the three positions with V/I. However I'm not sure how to find the inductive and capacitive reactance. Thanks for your help.
13. ### I Proof of Q=CV for arbitrarily shaped capacitors

What is a proof of the formula Q=CV for a capacitor with arbitrary but unchanging shape where C is a constant?
14. ### Resistor value given capacitance and EMF with a resistance R after 3ms

T=R/C So: 0.003s=R/100μC R=3*10^-7Ω I am really confused with the equations I have to use
15. ### Changing capacitance effect on ripple in full rectification circuit

[Mentor Note -- thread moved to the schoolwork forums] Hi. So I'm a Physics HL student in IB and I'm designing a circuit for my Physics IA. (think of it as a lab/project if you're not familiar with IB) I'm required to have an independent variable of 7 dif. values and a dependant variable. For...
16. ### Minimizing the voltage drop across a capacitor (solution shown)

The following is the question and the solution to the question. I understand the solution to the part where you find the Ceq and derive Qeq from the equation Q = Ceq*V. However, I do not understand where V1 = V0-V2 come from. When calculating the minimum voltage, how do you come up with the...
17. ### DC-DC conv. Ripple affecting Speech Recognition - Capacitance multiplier

Into a project I am working is use 12Vdc SMPS to power an audio amplifier and some more components. We have no “noise” on that stage. Then I use a step down converter to convert the 12V to 5V and power a mic preamplifier (Respeaker – usb Mic array) and a development board. There is a lot of...
18. ### B Basic questions regarding theory of electrical capacitance

Hello, all. First, I want to apologize if this is not the correct forum or area of the forum for this question. Please direct me if I should be posting this somewhere else. I have some questions regarding what I believe is best described as the "theory" of electrical capacitance. As my...
19. ### Capacitance of infinitely long coaxial cylinders of elliptical section

I've been able to prove the following inequality $$\frac{2\pi\epsilon_0}{\log\left(\frac{b_1b_2}{a_1^2}\right)}\leq C \leq \frac{2\pi\epsilon_0}{\log\left(\frac{a_1a_2}{b_1^2}\right)}$$ but have no clue how to obtain exact value. Can someone check whether this inequality is correct and show how...
20. ### Measuring Capacitance using a basic Multimeter

Is there any way to measure the capacitance of a capacitor indirectly using a multimeter that does not have the option to measure capacitance directly?
21. ### Equivalent Capacitance and Resistance of this Circuit

NOTE: THE C1 that is 120 microfarads is meant to be C3. What I did first was find equivalent capacitance of C2 and C3 by doing (40)*(120)/(40+120)=30. Then I found Ceq by doing (20)*(30)/(20+30)=12. For the resistance I did 6*3/(6+3)=2, for R2 and R1. Then to find Req I did (5)*(2)/5+2= 10/7 Am...
22. ### Calculating the speed of a JFET

Hello there, I believe here I need to find the capacitance of the junction between the P-doped gate and N-channel. Then I could find the RC time constant although I am not sure if there's something more I need to find the speed of the JFET? What I'm unsure of is the depletion width h to use...
23. ### I How can we prove that the capacitance does not depend on charge?

How could we prove mathematically that the capacitance does not depend on charge? I tried to find this proof in the internet but I was not able. Can you guys help me?
24. ### Comparing energy lost by the battery & energy gained by the capacitor.

Imagine the two terminal of a *parallel-plate capacitor* are connected to the two terminal of a battery with electric potential difference #V#. If the capacitance of the capacitor is #C#, and the area of each plate is $A$. In this process would the energy lost by the battery and the stored...
25. ### Engineering Capacitance for a capacitor with two dielectrics

The geometry of the capacitor can be either cylindrical or spherical.
26. ### Capacitance of a parallel-plate Capacitor with non uniform dielectric

Hey guys! I'm having trouble with the solution that I arrived at. Through boundary conditions I'm able to determine ##\vec{D}## as $$\vec{D}=-\frac{4Q}{R_0^2}\hat{e_z}$$ (In CGS units) Trough that I'm able to get the electric field as $$\vec{E}=-\frac{1}{\epsilon(r)}\frac{4Q}{R_0^2}\hat{e_z}$$...
27. ### Finding the capacitance of two separated hemispheres

like the picture, two adjacent hemispheres（radius R, distance d, assume the charge is ±Q of each side（assume evenly distributed）, can we calculate its capacitance?
28. ### LT spice result analysis, Capacitance Multiplier vs RC filter circuit

Hi friends, I have simulated two circuits, one is an RC filter and other is a Capacitance multiplier. My aim of experiment is to validate a decrease in Iout (load current) of CM circuit as compared to load current in RC filter circuit. Theoretically, Iout (CM circuit) < Iout (RC filter) Vp-p...
29. ### Harvesting the energy of sea waves using capacitance

Hello. I have a question related to capacitance. here is another mechanical solution to harness wave energy. Can changing capacity of the capacitor be used to harness wave energy? Let's say we envelope conductive plates in plastic and submerge them in the ocean and the water in between them...
30. ### Engineering Circuit theory: capacitor energy storage and discharging/charging times?

This is not my homework. I took it upon myself to answer a textbook question for mental stimulation. I wanted to know if someone can verify if these were the correct values that needed to be solved for, process, and final answer, and if not, what needed to be considered. For the initial...
31. ### Difficult capacitance problem -- 3 long concentric metal cylinders

A solution I found online claims that the effective capacitance between the middle and inner shell can be seen as: C (effective) = C1 + C2, where C1 is the capacitance between the inner and outermost shell, and C2 is the capacitance between the middle and outermost shell. Apparently C1 and C2...
32. ### Force needed to hold together a capacitor

I have 2 methods, which give 2 different solutions: Let sigma = charge per unit area Let plate 1 be the left plate, plate 2 = right plate. Method 1: Because they are insulating, consider the electric field at 3 regions; region 1 to the left of plate 1, region 2 between the plates, and region 3...
33. ### Engineering Depletion region capacitance in MOSFET

I would like to ask about the behavior of a MOSFET as a capacitor, particularly at the onset of inversion/weak inversion - see Fig 2.6(c) At this stage in Fig 2.6(c), there is positive charge at the gate metal/poly contact, then an insulator oxide and then negative ions (positive holes have...
34. ### Capacitance of a Sphere: A Quick Calculation Method

Could anyone tell me the capacitance of a one food diameter metal sphere. I know that this is a one terminal component but it still should have a capacitance. If a charge of Q is small and a 6 inch radius is drawn about the point then that 6 inch radius ( 12 in diameter ) should have a...
35. ### Understanding Energy Loss of 2 Joules in Circuits with Changing Capacitance

I am given the answer is 2J and I know how to get there with U = q^2/2C. But what I don't understand is that why is the energy not conserved here? How can energy loses just because the capacitance is doubled?
36. ### Engineering Calculate the Capacitance of 3 conductors in the presence of the ground

Initially, I thought to apply the image charge theorem, but I don't know how to continue. Someone could give me some indication on how to solve the problem? Thank you.
37. ### Coaxial cable - capacitance, leakage current and power lost

Could somebody check my solution?
38. ### Is capacitance more fundamental than resistance?

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...
39. ### Equivalent Capacitance of a Triangular Network of Capacitors

Hi, I'm struggling with this question. I feel like I don't even know where to begin. It seems to be a relatively simple calculation, but would the effective capacitance between A and C not just be 1 microFarad? Obviously that can't be the correct answer because such a simple observation wouldn't...
40. ### Find the capacitance of a half-full capacitor

The capacitance must be found, that is: ##C=\frac {Q}{V_a-V_b}##. Let ##\vec{E_d}## and ##\vec{E_v}## be the electric fields due to the zone with dielectric and the zone without dielectric respectively. In the case of a spherical capacitor with a vacuum between its plates, it is easy to...
41. ### A capacitor of variable capacitance

Using: i(t)=\frac{U}{R}.e^{-\frac{t}{RC}} As the power is constant, then the current will be constant, so: t/RC is constant I don't know how to proceed anymore. I think you should use some derivative, but I'm still very new to that part, so how can I proceed?
42. ### Understanding the Phase Difference Between Voltage & Current in a Circuit

Consider a circuit with a witch, capacitor and an AC voltage source. The sinusoidal AC voltage source is depicted in the following graph: We know that, ##Q = CV## ##\frac{dQ}{dt} = C \frac{dV}{dt}## ##i = C\frac{dV}{dt} \tag{1}## So from the graph, the voltage increases rapidly around ## t =...
43. ### Question about charged capacitors and inserting a dielectric into one

First when it is connected to the battery, the capacitors start accumulating charges such that the potential difference equals that of the battery. Then the current stops flowing. ##Q_1 = CV## ##Q_2 = nCV## Where 1 and 2 represent the capacitor with capacitance C and nC respectively Then, when...
44. ### Struggling to find the equivalent capacitance of this circuit

I asserted C3, C4, and C5 to be in series. **I found the capacitance of "C3-4-5" to be 1.67x10-6 F. This I did by using 1/C = 1/C3 + 1/C4 + 1/C5 Then I noticed that I had another series circuit of "C3-4-5" and C1, and C2. Again, I used a similar formula. I obtained an equivalent capacitance of...
45. ### Detecting the Alignment of an Inf. Plane Capacitor: A Paradox?

Assuming we have an infinite plane capacitor,where the upper plate is charged positively and the bottom layer is charged negatively. Now we know the field outside the capacitor is zero so we can't tell if the positive charge is on the upper plate or the lower plate. But, if we place it inside...
46. ### A 50 kW load operates from a 60 Hz 10 kV rms line with a power factor of 60% lagging -- Determine the capacitance that must be placed in parallel

Please can you have a look at the file at point me in the right direction if I'm wrong. Thank you
47. ### Capacitance of a spherical capacitor

When I try to do Gauss, the permeability is not always that of the free space, but it varies: up to a certain radius it is that of the void and then it is the relative one. How can I relate them? I'm trying to calculate the capacity of a spherical capacitor. The scheme looks like this: inside I...
48. ### Equivalent Capacitance Between X and Y in this capacitor circuit

This is the problem. If someone asks you this question, how would you solve it? I am finding it really tough to solve when the circuit gets a bit complex. It would be nice if you share what exactly you'll do to solve complex circuits such as this (the algorithm).

50. ### Kirchoff's laws and capacitance

Equivalent capacitance before and after remains the same. Now the 10F capacitor (which was initially connected in parallel with 20F) would have 30 C charge. Hence an additional 20C must have been supplied to it. The only path which may supply the charge is through battery. However this leads...