# Capacitance Definition and 146 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. ### 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?
2. ### 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...
3. ### 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...
4. ### 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?
5. ### 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...
6. ### 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...
7. ### Engineering Capacitance for a capacitor with two dielectrics

The geometry of the capacitor can be either cylindrical or spherical.
8. ### 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 $$\vec{E}=-\frac{1}{\epsilon(r)}\frac{4Q}{R_0^2}\hat{e_z}$$...
9. ### 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?
10. ### 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...
11. ### 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...
12. ### 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...
13. ### Purely Capacitive AC Circuit -- Seeking intuition for why why voltage lags behind current

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 =...
14. ### 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...
15. ### Detect if the Electric Field in a parallel plate capacitor is pointing up or down

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...

17. ### Electric field between two capacitor plates (proof)

See attached image
18. ### Frequency in an AC circuit given capacitance, voltage, and current

By combining the formula for the reactance of a capacitor with Ohm's Law for a capacitor, I can solve for angular frequency, and divide by 2π to find frequency. The resulting equation is: f = I/(2π VC) Using the given values, I end up with 5.2 kHz, instead of the correct answer of 5.2 MHz. I...
19. ### How to calculate Carrier Concentration vs. Depth from a CV measurement?

I'm trying to obtain the free carrier concentration vs depth profile from the CV (capacitance-voltage) measurements of a normally-on HEMT with the expressions used for a Schottky barrier, but I´'m confused about how to extract the values for depth. I found in textbooks and articles that the...
20. ### How to find the charge at time = t (at any instant)

I was not able to derive the charge on the capacitor. But then, I arbitrarily assumed ##\phi=B.A## (Dot product of Magnetic field and Area) Then, proceeding as follows, ##\phi=BA\cos(\omega_0 t)## ##\frac{d\phi}{dt}=−BA\omega_0\sin(\omega_0 t)## Now at ##t=0, \phi=BA\cos(0)=BA## Therefore...

Hello, I have made a capacitive water level sensor. It is a parallel plate capacitor. While measuring the capacitance of my sensor, I measure 53 pF. I then leave it for couple of minutes, still conected to the meter, capacitance then rises to 54 pF. Capacitance is slowly increasing. Why is...
22. ### Calculating the capacitance of a capacitor

Summary: Two plates side by side, not parallel to each other. Hello everyone, Purpose of this capacitor is to detect changes in water level. It is constructed of a single copper plated pcb on which middle I have made a 1 mm of space separating now two copper plates on a single pcb. So, plates...

33. ### RC Circuit - Rate energy is dissipated in the resistor

Homework Statement 1. A 2.01 uFcapacitor that is initially uncharged is connected in series with a 6.51 kΩ resistor and an emf source with 74.6 V and negligible internal resistance. The circuit is completed at t = 0. a) Just after the circuit is completed, what is the rate at which electrical...
34. ### Finding the energy density outside of an isolated charged sphere

Homework Statement A charged isolated metal sphere of diameter d has a potential V relative to V = 0 at infinity. Calculate the energy density in the electric field near the surface of the sphere. State your answer in terms of the given variables, using ε0 if necessary. Homework Equations...
35. ### Explaining a signal converting circuit

i have a drawing of a circuit that converts a signal in range [-5,5] V to a range [0,1.2]V . i wish to understand how it works.. i have basic knowledge of electricity as an undergraduate in general physics but a bit rusty , thus i am here looking for answers...
36. ### Spherical Capacitor Discharging Through Radial Resistor

Homework Statement A spherical capacitor has internal radius ##a## and external radius ##b##. At time ##t = 0##, the charge of the capacitor is ##Q_0## Then the two shells are connected by a resistor in the radial direction of resistance ##R##. Find the Poynting vector and the energy...
37. ### Combination of capacitors

Homework Statement Between the plates of parallel plate condenser having charge Q,a plate of thickness t1 and dielectric constant k1 is placed.In the rest of the space,there is another plate of thickness t2 and dielectric constant K2.The potential difference across the condenser will be...
38. ### Capacitor problem with a beam balance -- balancing after changing the charge

The lower plate of a parallel plate capacitor is supported on a rigid rod.The upper plate is suspended from one end of a balance.The two plates are joined together by a thin wire and subsequently disconnected.The balance is then counterpoised.Now a voltage V= 5000V is applied between the...
39. ### B Bonding energy in compounds

I have been researching on the bonding energies of different compounds, and for example, for CO2 it is 1600kJ/mole, 1600kJ/44g, or ~36.37kJ/g of energy required to split the carbon dioxide into carbon and oxygen. Furthermore, I transformed the amount of energy required in kJ to degrees celsius...
40. ### Capacitance of a sphere

Homework Statement Assume a conducting sphere has a radius of 3400km with an electric field of 100 V/m at it's surface. a) Calculate total charge of sphere. b)Calculate potential at the surface using infinity at reference point c) Calculate capacitance of the sphere using the result of a or b...
41. ### Which quantities are not the same for this capacitor setup?

Homework Statement Two parallel-plate capacitors with the same plate separation but different capacitance are connected in parallel to a battery. Both capacitors are filled with air. The quantity that is NOT the same for both capacitors when they are fully charged is: A. potential difference...
42. ### What happens to the capacitance after increasing distance?

Homework Statement A battery is used to charge a parallel-plate capacitor, after which it is disconnected. Then the plates are pulled apart to twice their original separation. This process will double the: A. capacitance B. surface charge density on each plate C. stored energy D. electric...
43. ### A Interface states in a PIN diode

Is the equation used to determine the density of interface states in schottky diodes from capacitance- frequency data applicable to PIN junctions?
44. ### Two like capacitors in parallel

I'm having a little trouble understanding capacitors in parallel and series. I understand that if there are two capacitors in a circuit with a potential difference Vab then the potential difference across the capacitors is also Vab. Every example I have seen have been for two capacitors with...
45. ### Dielectric inserted into a parallel plate capacitor

Homework Statement The capacitor (of thickness d) is disconnected from a potential source of V and a dielectric of thickness t is inserted and it has relative permitivity Er. Find the new potential between the plates Homework Equations [/B] This is the answer : Vf = V/d(d - t + t/Er) The...
46. ### Does the charge of a capacitor change during immersion?

If given a capacitor with stored charge, would its charge remain constant before and after it is immersed in a liquid (i.e. distilled water)? Why? I know that before immersion, the capacitance would be = (ɛAV/d), but would that be the same if immerged in distilled water?
47. ### Calculating how to make a homemade capacitor

Ok, so I am am trying to make a homemade capacitor that is 4700pf and 15kv. polyester at 125 micrometers thick can withstand 15kv so were good. here is the equation i used C=ε0 K A / D Where C = capacitance, ε0 is epsilons constant, K = dielectric constant, A = area of aluminum foil, and D is...
48. ### How do I calculate the capacitance of two unequal lines?

The capacitance formula for equal line is as follows. : * my question : I want to know the capacitance formula for unequal lines and its solving process . Thanks in advance for any hint.
49. ### Individual Charges and voltage

Homework Statement the capacitance of each capacitors and the cell voltage Homework Equations The Attempt at a Solution I got the total capacitance = 8028/5333 uF total voltage = 36v total charge=289008/5333 uC
50. ### Stray/Parasitic Capacitance - Impacts phase velocity?

Hey everyone, I'm trying to measure the stray capacitance in a circuit comprised of an rf signal generator, an oscilloscope, a coaxial cable (short-circuited) and some capacitors. I measured the resonant frequencies of the coaxil cable for varying values of capacity (0pF to 850pF) between 4MHz...