# capacitance Definition and Topics - 141 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. ### 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...
2. ### Engineering Capacitance for a capacitor with two dielectrics

The geometry of the capacitor can be either cylindrical or spherical.
3. ### 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 $$\vec{E}=-\frac{1}{\epsilon(r)}\frac{4Q}{R_0^2}\hat{e_z}$$...
4. ### 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?
5. ### 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...
6. ### 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...
7. ### 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...
8. ### 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 =...
9. ### 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...
10. ### 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...

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

See attached image
13. ### 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...
14. ### 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...
15. ### 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...
17. ### 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...

28. ### 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...
29. ### 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...
30. ### 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...