1.8.11 · D5 · HinglishElectromagnetism
Question bank — Capacitance — parallel plate derivation, cylindrical, spherical
1.8.11 · D5· Physics › Electromagnetism › Capacitance — parallel plate derivation, cylindrical, spheri
True or false — justify
Capacitance of a given capacitor doubles if you double the charge on it.
False. lekin double karne se field bhi double hoti hai aur isliye bhi exactly usi step mein double ho jaata hai, toh ratio unchanged rehta hai — sirf geometry aur dielectric se fix hota hai.
A capacitor with no charge on it has zero capacitance.
False. Capacitance hai jo ek ratio ke roop mein evaluate hota hai jo limit mein survive karta hai: yeh shape ki ek property hai, par bhi present rehti hai, bilkul jaise ek cup ka volume tab bhi exist karta hai jab cup khaali ho.
The two plates of a real capacitor carry the same charge.
False. Wo equal and opposite charge aur carry karte hain; "capacitor par charge" ka matlab positive plate par magnitude hai, net nahi (jo zero hota hai).
Filling the gap with a dielectric of constant always increases the capacitance.
True. Polarized dielectric field ko partially cancel karta hai, toh same se smaller produce hota hai, ko factor se badhata hai (dekho Dielectrics and Polarization).
For a spherical capacitor you can find by plugging the outer radius into .
False. yahan do shells ke beech potential ka difference hai, ; ek akela ek akele charge ka potential hai, do-conductor gap ka nahi.
Cylindrical capacitance scales as , just like the plate scales as .
False. Coaxial field ki tarah girta hai, isliye integrate karne par ek logarithm milta hai: . Sirf plate ka uniform field ek plain gap tak integrate hota hai.
An isolated single sphere has no capacitance because there's only one conductor.
False. Uski "second plate" infinity hai; mein lene par finite value milti hai.
At fixed charge , pushing parallel plates closer together stores more energy.
False. Chhota matlab bada , aur girta hai; energy actually decrease hoti hai, isliye plates attract karti hain (unhe alag karna hi kaam leta hai).
Spot the error
"Field between plates is , because that's a single charged sheet."
Factor-2 ka error hai. Do opposite-charged plates ke beech do sheet fields add hote hain, dete hain; Gauss's Law mein pillbox already yeh bake in karta hai kyunki flux sirf inner face se baahir jaata hai.
" from − plate to + plate gives the capacitor voltage."
Sign slip hai. Field ke against jaana (− se +) negative number deta hai; positive magnitude paane ke liye + plate se − plate tak (field ke along) integrate karna hoga.
"For the coaxial cable I set the Gaussian cylinder area to ."
Galat geometry ka area hai. Cylinder ke curved side ka area hota hai; ek sphere ka hai. Galat area use karne se field kharab ho jaata hai.
" works even when is comparable to the plate width."
Fringing ko ignore karta hai. Formula ideal uniform field assume karta hai (); jab bada ho toh edges par fringe fields capacitance add karte hain, isliye formula ko underestimate karta hai.
"Doubling the plate area doubles the field for the same charge."
Ulta hai. Fixed ke liye, double karne se aur isliye half ho jaata hai; field kamzor hoti hai, aur yahi reason hai ki , ke saath badhta hai.
"In the spherical derivation I use ."
Galat antiderivative hai. hai (yeh field hai); woh hai jo cylindrical field deta hai.
Why questions
Why does always cancel in every capacitance derivation?
Kyunki field charge mein linear hoti hai ( Gauss's law se) aur bhi, isliye ratio mein koi nahi bachta — proof ki capacitance pure geometry hai.
Why is the parallel-plate field independent of position inside the gap?
Pillbox Gaussian area Gauss's law ke dono taraf cancel ho jaata hai, chhodta hai jisme koi ya nahi — infinite-plane field ki pehchaan.
Why does the coaxial capacitor produce a logarithm but the sphere a ?
Unki fields alag tarah se fall off karti hain: integrate hokar deta hai, jabki integrate hokar deta hai; Gaussian surface ki geometry (uske area ka -power) field ke -power ko aur isliye integral ko dictate karta hai.
Why do we say capacitance measures how "generous" a conductor pair is?
High- pair apna voltage ("push-back") zyada badhne se pehle bahut saara charge swallow karta hai — ka matlab hai bada deta hai bada per volt, bilkul woh intuition jo Electric Potential mein hai.
Why does a thin high- film beat a huge air gap for making big capacitors?
chhhote aur bade ko reward karta hai; dielectric wala rolled thin film dono ko maximize karta hai, isliye nanofarads ek tiny package mein microfarads ban jaate hain.
Why does making the outer coax conductor bigger (larger ) decrease the capacitance?
Bada ko increase karta hai, jo denominator mein hota hai, isliye shrink hota hai — wider gap matlab charge per unit ke liye zyada voltage climb karna.
Edge cases
What happens to the spherical capacitance as (shells almost touching)?
: vanishing gap ko blow up karta hai, plate intuition se match karta hai ki tiny separation huge capacitance deta hai.
What is the capacitance of a spherical capacitor as ?
Yeh tend karta hai — ek isolated sphere ki finite capacitance, kyunki outer "plate" infinity par chali jaati hai lekin inner sphere abhi bhi finite voltage par charge hold karta hai.
What happens to any capacitor's field and voltage as ?
Dono saath zero par jaate hain, lekin unka ratio rehta hai; geometry-defined capacitance well-defined limit hai chahe numerator aur denominator dono vanish kar rahein hon.
If two identical capacitors are wired in series, is the combined capacitance bigger or smaller than one alone?
Smaller — series capacitors reciprocally add karte hain, yahan half value dete hain, kyunki same charge ko do voltage gaps climb karne padte hain (dekho Capacitors in Series and Parallel).
For the coaxial cable, what does physically mean for a real transmission line?
Cable ka har extra metre same fixed capacitance add karta hai, isliye ek lamba line proportionally zyada charge per volt store/couple karta hai — Coaxial Cable Transmission Lines mein ek key spec.
What limits how much energy a capacitor can hold before it fails?
Dielectric ka breakdown field: badhane se badhta hai jab tak insulator ionize nahi ho jaata aur spark across nahi ho jaata, isliye aur material — formula nahi — ceiling set karte hain.
Recall One-line self-test
Har answer chhupa lo, phir jawab do: kya , par depend karta hai, par, ya kisi par nahi? Kisi par nahi — sirf geometry aur dielectric. ::: Sahi hai agar tumne reason bhi bola: aur dono ke saath scale karte hain, isliye ratio -free hai.