Foundations — Series and parallel capacitors — derivations

1.8.12 · D1 · Physics › Electromagnetism › Series and parallel capacitors — derivations

Yeh page har woh symbol build karta hai jis par parent note depend karta hai, bilkul zero se. Neeche kuch bhi yeh assume nahi karta ki tumne pehle kabhi capacitor dekha hai. Upar se neeche padho — har idea agli ke liye ek brick hai.

1. Charge — symbol $Q$

Picture: socho ek metal plate hai. Agar hum uspe kuch extra electrons scrape karke daalen, toh plate negative charge carry karti hai; agar electrons nikaal lein, toh positive charge carry karti hai. $Q$ bas "kitna extra" ka score-keeper hai.

Topic ko yeh kyun chahiye: capacitor ka poora point $Q$ store karna hai. Har derivation "yahan kitna charge baitha hai?" se shuru hoti hai. Charge conservation dekho us rule ke liye ki charge kabhi create ya destroy nahi hota — hum yeh series proof mein use karenge.

2. Voltage — symbol $V$

Picture: socho alag-alag heights par do paani ke tanks hain. Paani chahta hai high se low ki taraf flow kare. Height ka difference hi "pressure" = voltage hai. Battery ek pump hai jo ek side ko permanently upar rakhhti hai.

Topic ko yeh kyun chahiye: parent note ka key sentence "parallel = same $V$, series = same $Q$" poori tarah voltage ke baare mein hai. "Same voltage" ka exact matlab samajhna zaroori hai us sentence ke make sense hone se pehle.

3. Capacitor aur uski plates

Picture: do flat sheets ek doosre ke samne thin gap ke saath. Ek positive ho jaati hai, doosri exactly utni hi negative — gap charge ko cross nahi karne deta, isliye plates $+Q$ aur $-Q$ par balanced rehti hain.

Aksar gap mein storage badhane ke liye ek insulating material bhari jaati hai — dekho Dielectrics in capacitors.

4. Master rule — $Q=CV$

Picture: capacitance ek bucket ki chaurai hai. Chauri bucket (bada $C$) bahut saara paani (charge $Q$) hold karti hai jabki paani ka level (voltage $V$) mushkil se barhta hai. Patli bucket thode paani se hi ucha level fill kar leti hai.

5. Wires, nodes, aur "same voltage"

Picture: wire ek bilkul flat, level lake hai. Usmein kahin bhi ek patta daalo — har jagah same paani ki height. Do plates jo same node se wire hain unhe same electrical "height" par force kiya jaata hai.

Topic ko yeh kyun chahiye: parent ka parallel proof "$V_1=V_2=V_3=V$" se shuru hota hai. Woh line equipotential wires aur nodes ki wajah se hi valid hai.

6. Do conservation laws jis par hum rely karenge

Picture: ek road fork. Har gaadi jo junction mein enter karti hai kisi na kisi branch se nikalni chahiye — koi gayab nahi hoti. Parallel proof mein yeh battery ka charge branches mein split karta hai: $Q=Q_1+Q_2+Q_3$.

Picture: ek hiking loop. Chahe kitne bhi ups aur downs hon, jab tum camp wapas aate ho tumhara net height change zero hai. Series proof mein yeh deta hai $V=V_1+V_2+V_3$.

7. Equivalent capacitance $C_{eq}$

Topic ko yeh kyun chahiye: yeh literally woh answer hai jisko dono derivations dhundh rahi hain. Baaki sab is ek number ko compute karne ka zariya hai.

8. Reciprocals — symbol $1/C$

Prerequisite map

Equipment checklist

Right side cover karo; answer do, phir reveal karo.