sandhaaritr

vibhinn prakaar ke aadhunik sandhaaritr

samaantar plate sandhaaritr ka ek saral roop

sandhaaritr ya kaipesitr (Capacitor), vidyut paripth mein prayukt hone wala do siron wala ek pramukh avayav hai. yadi do ya do se adhik chaalakon ko ek vidyutrodhi maadhyam dvaara alag karke sameep rakha jaae, to yeh vyavastha sandhaaritr kahalaati hai. in chaalakon par baraabar tatha vipreet aavesh hote hain. yadi sandhaaritr ko ek baitari se joda jaae, to ismein se dhaara ka pravaah naheen hoga, parantu iski pleton par baraabar maatra mein ghanaatmak evam rinaatmak aavesh sanchaya ho jaaeainge. vidyut sandhaaritr ka upayog vidyut aavesh, athva sthir vaidyut urja, ka sanchaya karne ke liye tatha vaidyut filtar, snabar (shakti ilektrauniki) aadi mein hota hai.

sandhaaritr mein dhaatu ki do pletein hoteen hain jinke beech ke sthaan mein koi kuchaalak daaielektrik padaarth (jaise kaagaj, pauleetheen, maaika aadi) bhara hota hai. sandhaaritr ke pleton ke beech dhaara ka pravaah tabhi hota hai jab iske donon pleton ke beech ka vibhvaantar samay ke saath badle. is kaaran niyat deesi vibhvaantar lagaane par sthaayi avastha mein sandhaaritr mein koi dhaara naheen bahti. kintu sandhaaritr ke dono siron ke beech pratyaavarti vibhvaantar lagaane par uske pleton par sanchit aavesh kam ya adhik hota rahata hai jiske kaaran vaahya paripth mein dhaara bahti hai. sandhaaritr se hokar deesi dhaara nahi bah sakti.

sandhaaritr ki dhaara aur uske pleton ke beech mein vibhvaantar ka sambandh nimnaankit sameekaran se diya jaata hai-

I=C{dU \over dt}

jahaaain :

I sandhaaritr ke pleton ke beech bahne waali dhaara hai,
U sandhaaritr ke pleton ke beech ka vibhvaantar hai,
C sandhaaritr ki dhaarita hai jo sandhaaritr ke pleton ki doori, unke beech prayukt daaielektrik padaarth, pleton ka kshetrafal evam anya jyaamiteeya baaton par nirbhar karta hai. sandhaaritr ki dhaarita nimnalikhit sameekaran se paribhaashit hai-

Q=C\cdot U

anukram

sandhaaritr mein sangrahit oorja

sandhaaritr ko aaveshit karne mein jo kaarya karna padta hai vah sandhaaritr mein sangrahit ho jaati hai. sandhaaritr mein sangrahit yeh oorja vidyut kshetr ke roop mein hoti hai. sangrahit oorja U ka maan nimnalikhit sootr dvaara abhivyakt hoti hai-

W={\frac {1}{2}}CV^{2}={\frac {1}{2}}VQ={\frac {1}{2}}{\frac {Q^{2}}{C}}=U_{\text{stored}}

vaidyut kshetr ke kisi bindu par ikaai aayatan mein sangrahit urja ka maan nimnalikhit sootr se diya ja sakta hai-

\,u={\frac {1}{2}}\epsilon _{0}E^{2}

sandhaaritron ke pramukh upayog

urja bhandaaran ke liye
shakti gunaank ko behtar banaane ke liye
vibhinn vidyut filtaron mein
vidyut paripthon mein samay-sambandhi paripth (timing circuit) banaane ke liye
pals-power evam shastr nirmaan
censor ke roop mein (jaise CVT = kaipesitiv voltej traansafaurmar)

sandhaaritron ke upayog

sandhaaritron ka sanyojan

jis prakaar pratirodhon aur prerakatvon ko aavashyakataanusaar shreneekram ya samaantar kram mein jodkar uchit maan (vailyoo) tatha uchit rating (vaatej, voltata, dhaara ki rating aadi) praapt kar li jaati hai, usi prakaar do ya adhik sandhaaritron ko bhi aavashyakataanusaar sanyojit kiya jaata hai.

shreneekram mein sanyojan

shreneekram mein jude hue n sandhaaritron ka tulya dhaarita nimnalikhit sootr se di jaati hai:

{1 \over C_{z}}={1 \over C_{1}}+{1 \over C_{2}}+...+{1 \over C_{n}}=\sum _{i=1}^{n}{1 \over C_{i}}

do sandhaaritr shreneekram mein jode jaaainya to unki tulya dhaarita nimnalikhit saral sootr se nikaala ja sakta hai-

C_{z}={C_{1}C_{2} \over C_{1}+C_{2}}

aur agar dono sandhaaritr samaan maan vaale hon to shreneekram mein sanyojit karne par unki tulya dhaarita pratyek ki dhaarita ki aadhi ho jaati hai. udaaharan ke liye 10 maaikrofairaad ke do sandhaaritron ko shreneekram mein jodne par tulya dhaarita 5 maaikrofairaad hogi.

samaantarakram mein sanyojan

samaantar kram mein jude sandhaaritron ki kul dhaarita (tulya dhaarita) unki dhaaritaaon ke yog ke baraabar hoti hai.

C_{z}=C_{1}+C_{2}+...+C_{n}=\sum _{i=1}^{n}C_{i}

udaaharan ke liye 10 maaikrofairaad vaale 4 sandhaaritr samaantarakram mein jod diye jaaainya to unki kul dhaarita 40 maaikrofairaad ho jaaegi.

kuchh pramukh sandhaaritr sanrachanaaen

sandhaaritr ki do pleton (chaalakon) ka sanyojan (areinjament) tarah-tarah se kiya ja sakta hai. is prakaar sandhaaritr bhi kai tarah ke hote hain. teen mukhya jyaamiti vaale sandhaaritron ke baare mein neeche ki saarani mein mukhya jaanakaariyaaain di gayeen hain. sandhaaritr ke do chaalakon (pleton) ke beech ke kuchaalak ki ek mukhya gun usaki paramitiviti (permitivity) hai jo ε se niroopit ki jaati hai. nirvaat ki paramitiviti ko ε₀ se nirupit kiya jaata hai. iska maan hai:

\varepsilon _{0}=8{,}8542\cdot 10^{-12}\;\mathrm {F/m}

prakaar	dhaarita	vidyut kshetr	chitr
samaantar plate sandhaaritr	$C=\varepsilon _{0}\varepsilon _{\mathrm {r} }\cdot {\frac {A}{d}}$ $C=\varepsilon _{0}\varepsilon _{\mathrm {r} }\cdot {\frac {A}{d}}$	$E={\frac {Q}{\varepsilon _{0}\varepsilon _{\mathrm {r} }A}}$ $E={\frac {Q}{\varepsilon _{0}\varepsilon _{\mathrm {r} }A}}$
belanaakaar sandhaaritr	$C=2\pi \varepsilon _{0}\varepsilon _{\mathrm {r} }\,{\frac {l}{\ln \!\left({\frac {R_{2}}{R_{1}}}\right)}}$ $C=2\pi \varepsilon _{0}\varepsilon _{\mathrm {r} }\,{\frac {l}{\ln \!\left({\frac {R_{2}}{R_{1}}}\right)}}$	$E(r)={\frac {Q}{2\pi rl\varepsilon _{0}\varepsilon _{\mathrm {r} }}}$ $E(r)={\frac {Q}{2\pi rl\varepsilon _{0}\varepsilon _{\mathrm {r} }}}$
goleeya sandhaaritr	$C=4\pi \varepsilon _{0}\varepsilon _{\mathrm {r} }\left({\frac {1}{R_{1}}}-{\frac {1}{R_{2}}}\right)^{-1}$ $C=4\pi \varepsilon _{0}\varepsilon _{\mathrm {r} }\left({\frac {1}{R_{1}}}-{\frac {1}{R_{2}}}\right)^{-1}$	$E(r)={\frac {Q}{4\pi r^{2}\varepsilon _{0}\varepsilon _{\mathrm {r} }}}$ $E(r)={\frac {Q}{4\pi r^{2}\varepsilon _{0}\varepsilon _{\mathrm {r} }}}$
geind	$C=4\pi \varepsilon _{0}\varepsilon _{\mathrm {r} }R_{1}$ $C=4\pi \varepsilon _{0}\varepsilon _{\mathrm {r} }R_{1}$
samaantar belan (lekar-line Lecher lines)	$C={\frac {\pi \varepsilon l}{\rm {arcosh\left({\frac {d}{2R}}\right)}}}$ $C={\frac {\pi \varepsilon l}{\rm {arcosh\left({\frac {d}{2R}}\right)}}}$
samatal plate ke samaantar belan	$C={\frac {2\pi \varepsilon l}{\operatorname {arcosh} \left({\frac {d}{R}}\right)}}$ $C={\frac {2\pi \varepsilon l}{\operatorname {arcosh} \left({\frac {d}{R}}\right)}}$		d > R
a trijya vaale do gole	$C=2\pi \varepsilon a\left\{\ln 2+\gamma -{\frac {1}{2}}\ln \left({\frac {d}{a}}-2\right)+O\left({\frac {d}{a}}-2\right)\right\}$ $C=2\pi \varepsilon a\left\{\ln 2+\gamma -{\frac {1}{2}}\ln \left({\frac {d}{a}}-2\right)+O\left({\frac {d}{a}}-2\right)\right\}$