क्यापासिट्यान्स

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क्यापासिट्यान्स छगू बियातःगु इलेक्ट्रिकल पोटेन्सियलय् स्वथनातःगु (वा बायातःगु) इलेक्ट्रिकल चार्जया मात्राया आंकलन ख। थुकिया दक्ले साधारण रुप टु-प्लेट क्यापासिटर ख। यदि प्लेटय् दूगु चार्ज +Q व −Q, व V प्लेटतेगु दथुया भोल्ट जुसा, क्यापासिट्यान्स थ्व कथं लिकायेछिं

C={\frac {Q}{V}}

क्यापासिट्यान्सया एस आइ युनिट फराड ख; १ फराड = १ कोलुम्ब प्रति भोल्ट।

उर्जा

क्यापासिटरय् मुंकातःगु उर्जा (जुलय् लनिगु) थुकियात चार्ज यायेत याःगु ज्या बराबर जुइ। छगू क्यापासिटेन्स C , छगू प्लेटय् चार्ज +q व मेगु प्लेटय् -q तयातःगु बिचाः यानादिसँ। चार्जया चिधंगु तत्त्वयात $\mathrm {d} q$ छगू प्लेटं मेगु प्लेटय् पोटेन्शियल डिफरेन्स V = q/C विरुद्ध यायेमाःगु ज्या $\mathrm {d} W$ :

\mathrm {d} W={\frac {q}{C}}\,\mathrm {d} q

गन

W धयागु जूलय् दाना स्वइगु ज्या खः

q धयागु कुलोम्बय् दाना स्वइगु चार्ज खः

C धयागु क्यापासिटेन्स खः, गुकियात फाराडय् दाना स्वइ

थुगु समीकरणयात एकीकृत यानाः झीसं क्यापासिटेन्सय् मुंकातःगु उर्जा लुइके फै । अनचार्ज क्यापासिटेन्स (q=0) निसें न्ह्याकेगु व प्लेटय् चार्ज +Q व -Q मवःतले छगू प्लेटं मेगु प्लेटय् चार्ज यंकेगु ज्या W:

W_{charging}=\int _{0}^{Q}{\frac {q}{C}}\,\mathrm {d} q={\frac {1}{2}}{\frac {Q^{2}}{C}}={\frac {1}{2}}CV^{2}=W_{stored}

फ्लाट-प्लेट क्यापासिटरया क्यापासिटेन्सया निंतिं थुकियात च्वय् बियातःगु समीकरणलिसे स्वानाः झीसं कायेखनी :

W_{stored}={\frac {1}{2}}CV^{2}={\frac {1}{2}}\epsilon {\frac {A}{d}}V^{2}

गन

W धयागु जूलय् दाना स्वइगु उर्जा खः।

C धयागु क्यापासिटेन्स खः, गुकियात फाराडय् दाना स्वइ।

V धयागु भोल्टय् दाना स्वइगु भोल्टेज खः।

क्यापासिट्यान्स व 'डिस्प्लेस्मेन्ट करेन्ट'

भौतिकविज्ञान शास्त्री जेम्स क्लार्क म्याक्सवेलं विस्थापन करेन्टया अवधारणा दयेकादिल, ${\frac {\partial {\vec {D}}}{\partial t}}$ , गुकिलिं चार्ज मुंकाच्वंगु अवस्थाय्, दसु क्यापासिटरय्, चार्जया संरक्षणनाप एम्पियरया नियमयात ज्व नयेगु ज्या यात। वय्कलं थ्वयात, दक्व थासय् (भ्याकुमय् नं) चार्जया वास्तविक गतिया रुपय् व्याख्या यानादिल। वय्कलं थ्वयात ईथरय् दाइपोल चार्जया गतिनाप मेल खनि धकाः अनुमान यानादिल। वर्तमान भौतिकशास्त्रय् थ्व व्याख्या त्वःते धुंकूसां म्याक्सवेलं एम्पेयरया नियमय् याःगु सुधार धाःसा मान्य जुयाच्वंगु दु (हिलाच्वंगु विद्युत क्षेत्रं चुम्बकीय क्षेत्र दयेकी)।

म्याक्सवेलया समीकरणयात एम्पियरया नियमयात विस्थापन करेन्ट अवधारणालिसे स्वानाः थुकथं बियातःगु दु ${\vec {\nabla }}\times {\vec {H}}={\vec {J}}+{\frac {\partial {\vec {D}}}{\partial t}}$ । (निगुलिं पक्षयात एकीकृत यानाः, ${\vec {\nabla }}\times {\vec {H}}$ यात हिलेछिं — स्टोक्सया प्रमेयया सौजन्यं — ${\vec {H}}\cdot \mathrm {d} {\vec {l}}$ या इन्टिग्रल छगू बन्द काउन्टरय्, गुकिलिं एम्पियरया फर्मुलेसनया इन्तरकनेक्सन क्यनि। )

कोइफिसियन्ट अफ पोटेन्सियल

The discussion above is limited to the case of two conducting plates, although of arbitrary size and shape. The definition C=Q/V still holds if only one plate is given a charge, provided that we recognize that the field lines produced by that charge terminate as if the plate were at the center of an oppositely charged sphere at infinity.

C=Q/V does not apply when there are more than two charged plates, or when the net charge on the two plates is non-zero. To handle this case, Maxwell introduced his "coefficients of potential". If three plates are given charges $Q_{1},Q_{2},Q_{3}$ , then the voltage of plate 1 is given by

V_{1}=p_{11}Q_{1}+p_{12}Q_{2}+p_{13}Q_{3}

,

and similarly for the other voltages. Maxwell showed that the coefficients of potential are symmetric, so that $p_{12}=p_{21}$ , etc.

क्यापासिट्यान्स/इन्डक्ट्यान्स द्वैधता

गणितीय पदय् आदर्श क्यापासिटेन्सयात आदर्श इन्डक्टेन्सया उल्टा कथं कायेछिं , छाय् धाःसा निगु घटनाया भोल्टेज-करेन्ट समीकरणयात भोल्टेज व करेन्ट पदया आदानप्रदान याना छगू मेगुलिइ हिलेछिं।

सेल्फ-क्यापासिट्यान्स

In electrical circuits, the term capacitance is usually a shorthand for the mutual capacitance between two adjacent conductors, such as the two plates of a capacitor. There also exists a property called self-capacitance, which is the amount of electrical charge that must be added to an isolated conductor to raise its electrical potential by one volt. The reference point for this potential is a theoretical hollow conducting sphere, of infinite radius, centred on the conductor. Using this method, the self-capacitance of a conducting sphere of radius R is given by:

C=4\pi \epsilon _{0}R\,

[१]

Typical values of self-capacitance are:

for the top "plate" of a van de Graaf generator, typically a sphere 20 cm in radius: 20 pF
the planet Earth: about 710 µF

इल्यास्ट्यान्स

The inverse of capacitance is called elastance, and its unit is the reciprocal farad.

स्ट्रे क्यापासिट्यान्स

Any two adjacent conductors can be considered as a capacitor, although the capacitance will be small unless the conductors are close together or long. This (unwanted) effect is termed "stray capacitance". Stray capacitance can allow signals to leak between otherwise isolated circuits (an effect called crosstalk), and it can be a limiting factor for proper functioning of circuits at high frequency.

Stray capacitance is often encountered in amplifier circuits in the form of "feedthrough" capacitance that interconnects the input and output nodes (both defined relative to a common ground). It is often convenient for analytical purposes to replace this capacitance with a combination of one input-to-ground capacitance and one output-to-ground capacitance. (The original configuration — including the input-to-output capacitance — is often referred to as a pi-configuration.) Miller's theorem can be used to effect this replacement. Miller's theorem states that, if the gain ratio of two nodes is 1:K, then an impedance of Z connecting the two nodes can be replaced with a Z/(1-k) impedance between the first node and ground and a KZ/(K-1) impedance between the second node and ground. (Since impedance varies inversely with capacitance, the internode capacitance, C, will be seen to have been replaced by a capacitance of KC from input to ground and a capacitance of (K-1)C/K from output to ground.) When the input-to-output gain is very large, the equivalent input-to-ground impedance is very small while the output-to-ground impedance is essentially equal to the original (input-to-output) impedance.

क्यापासिटर

मू पौ: क्यापासिटर

The capacitance of the majority of capacitors used in electronic circuits is several orders of magnitude smaller than the farad. The most common subunits of capacitance in use today are the millifarad (mF), microfarad (µF), the nanofarad (nF) and the picofarad (pF)

The capacitance can be calculated if the geometry of the conductors and the dielectric properties of the insulator between the conductors are known. For example, the capacitance of a parallel-plate capacitor constructed of two parallel plates of area A separated by a distance d is approximately equal to the following:

C=\epsilon _{r}\epsilon _{0}{\frac {A}{d}}

(in SI units)

where

C is the capacitance in farads, F

A is the area of each plate, measured in square metres

ε_r is the relative static permittivity (sometimes called the dielectric constant) of the material between the plates, (vacuum =1)

ε₀ is the permittivity of free space where ε₀ = 8.854x10^-12 F/m

d is the separation between the plates, measured in metres

The equation is a good approximation if d is small compared to the other dimensions of the plates. In CGS units the equation has the form:

C=\epsilon _{r}{\frac {A}{d}}

where C in this case has the units of length.

The dielectric constant for a number of very useful dielectrics changes as a function of the applied electrical field, e.g. ferroelectric materials, so the capacitance for these devices is no longer purely a function of device geometry. If a capacitor is driven with a sinusoidal voltage, the dielectric constant, or more accurately referred to as the relative static permittivity, is a function of frequency. A changing dielectric constant with frequency is referred to as a dielectric dispersion, and is governed by dielectric relaxation processes, such as Debye relaxationcapacitance.

फूटनोट

स्वयादिसँ

लिधंसा

Tipler, Paul (1998). Physics for Scientists and Engineers: Vol. 2: Electricity and Magnetism, Light (4th ed.). W. H. Freeman. ISBN 1-57259-492-6
Serway, Raymond; Jewett, John (2003). Physics for Scientists and Engineers (6 ed.). Brooks Cole. ISBN 0-534-40842-7
Saslow, Wayne M.(2002). Electricity, Magnetism, and Light. Thomson Learning. ISBN 0-12-619455-6. See Chapter 8, and especially pp.255-259 for coefficients of potential.

पिनेया स्वापू

Miller's Theorem