Capacitance


Previously Asked Questions

Q:    "Why is the total (equivalent) capacitance of a series connection always smaller than each of the capacitors connected in series?"

A:  Look at a simple example when only two capacitors are connected in series. Then, the formula for the total (equivalent) capacitance is:

1/Ceq = 1/C1 + 1/C2 - equ1.gif (246 bytes)

1/Ceq = 1/C1 + 1/C2 = (C1 + C2)/C1C2 - equ2.gif (269 bytes)

equ3.gif (1557 bytes)

You can verify that Ceq is less than any of the capacitors connected in series by trying the case of three capacitors, or four capacitors, etc.   Do the algebra correctly, and you will always obtain Ceq expressed as the product of any of the individual capacitors and a factor that is less than 1 (a ratio with the denominator larger than the numerator).

Q:     What does an electrical capacitor store?

A:     An electrical capacitor stores a "charge Q."  An electrical capacitor is defined as two conducting components separated from each other and charged with different amounts of charge, Q1 and Q2.  The "charge stored in a capacitor", Q, is the charge imbalance between the two components: Q = delta.gif (839 bytes)QQ2 - Q1.

It is also correct to say that an electrical capacitor stores energy.  Since the two conducting components of the capacitor are charged with different amounts of charge, Q1 and Q2,   an electric field exists between them, and an electric field stores energy within the space in which the electric field exists (within the volume in space defined by the geometric arrangement, with respect to each other, of the two conducting components of the capacitor.)

Q:     Many electronic devices carry a warning that removing the case, even with the power turned off, may cause electric shock.  Does this have anything to do with capacitors?  Why don't they discharge as soon as the power is cut?

A:     When the power of the circuit is turned off, capacitors may remain charged because not all electrodes are grounded.  If one touches the charged electrode one receives an electric shock caused by the discharge of this electrode through the human body.

Q:     Is it possible to break a capacitor by placing to much charge on it?

A:     Yes.   To place too much "charge" on a capacitor means to establish a too high potential difference,  delta.gif (839 bytes)V, between its conducting components.  If this potential difference is above what is called "breakage potential," an electric discharge results, destroying the capacitor.  If the capacitor contains an insulator between its conducting components, the insulator will be "burnt" at the atomic/molecular level.  A capacitor subjected to voltages exceeding the "breakage potential" cannot be recovered.  It should be discarded and replaced.  The value of  the "breakage potential" is given on a label attached to commercially available capacitors.

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References

Equations

Capacitance

C = q/V

Capacitance for a parallel-plate capacitor

26-9.gif (164 bytes)

Capacitance for a cylindrical capacitor

26-14.gif (264 bytes)

Capacitance for a spherical capacitor

26-17.gif (229 bytes)

Capacitance of an isolated sphere

C = 4pi2.gif (831 bytes) epsilon2.gif (824 bytes) 0R

Equivalent capacitance of capacitors connected in parallel

26-19.gif (200 bytes)

Equivalent capacitance of capacitors connected in series

26-20.gif (236 bytes)

Electric potential energy of a charge capacitor

26-21.gif (252 bytes)

Energy density (potential energy per unit volume)

u = onehalf.gif (67 bytes) epsilon2.gif (824 bytes) 0 E2

Gauss' Law with a dielectric

26-38.gif (216 bytes)

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List of Topics

Measurements Electric Potential Magnetism Electrical Circuits (AC) Optical Instruments: Mirrors and Lenses
Electrostatics Capacitance Sources of Magnetic Fields Maxwell's Equations Interference
Electric Fields Current and Resistance Magnetism in Matter Electromagnetic Waves Diffraction
Electric Flux Electrical Circuits (DC) Electromagnetic Induction Interaction of Radiation with Matter: Reflection, Refraction, Polarization  

 

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