Kirchhoff's current law (KCL), Kirchhoff's voltage law (KVL): Foundations

1.8.18 · D1 · Physics › Electromagnetism › Kirchhoff's current law (KCL), Kirchhoff's voltage law (KVL)

Is page par assume kiya gaya hai ki tumne kuch bhi nahi dekha. Parent note Kirchhoff's Laws padhne se pehle, tumhe genuinely feel karna hoga ki har squiggle ka matlab kya hai. Hum inhe ek ek karke, ek ke upar doosra, build karte hain.

1. Charge — woh cheez jo flow karti hai

Picture: socho ek bucket mein kuch paani hai. Bucket mein litres ki sankhya waisi hi hai jaise charge ki miqdar $Q$ . Zyada ya kam ho sakta hai, lekin litres jadugarni tarah appear ya vanish nahi hote — sirf ek jagah se doosri jagah move hote hain.

Topic ko yeh kyun chahiye: KCL literally yeh statement hai ki "charge kisi junction par appear ya vanish nahi hota." Tum woh sentence tab tak samajh nahi sakte jab tak $Q$ tumhare liye kuch concrete na ho.

2. Current — charge kitni tez flow karta hai

$I = \frac{Δ Q}{Δ t}$

Ise zor se padho: "current, charge mein change $Δ Q$ , divided by usmein lagi time $Δ t$ , ke barabar hai." Symbol $Δ$ (Greek letter delta) "mein change" ka shorthand hai — baad wali value minus pehle wali value. Toh $Δ Q$ = (abhi charge) − (thodi der pehle charge).

Figure — Kirchhoff's current law (KCL), Kirchhoff's voltage law (KVL)

Ek amount ki jagah rate kyun? Kyunki circuits flow ke baare mein hain. Ek wire ko parwah nahi ki usme ab tak kitna total charge gaya — usse parwah hai ki charge abhi kitni tez stream ho raha hai. Woh "per second" hi exactly $I$ ko current banata hai (yeh word ek river current se hi aaya hai).

3. Derivative — "instantaneous rate"

Parent note $\frac{d Q}{d t}$ likhta hai, $\frac{Δ Q}{Δ t}$ nahi. $Δ$ se $d$ par switch kyun?

Hame yeh sharper tool kyun chahiye? $Δ t$ ke kuch visible chunk hone par (maan lo poora ek second), agar flow speed up ya slow down ho rahi hai toh tum sirf us second par uska average paate ho. Letter $d$ ek alag, sharper sawaal ka jawab deta hai: "bilkul is precise moment par charge kitni tez badal raha hai?" KCL ki derivation ke liye hum is instant-by-instant rate ko zero set karte hain, isliye hamen instant version chahiye.

4. Node aur Loop — do shapes jinpar hum bookkeeping karte hain

Exactly yeh do hi kyun? Kyunki har conservation law unme se ek par rehti hai:

Charge conservation → node par apply hoti hai (wahan kuch pile up nahi hota) → KCL.
Energy conservation → loop ke around apply hoti hai (round-trip net zero deta hai) → KVL.

Kisi diagram mein nodes aur loops spot karna seekh lo aur circuit analysis ka aadha kaam pehle hi ho jaata hai.

5. Electric potential aur voltage — "electrical height"

Picture: ek pahadi landscape socho. Upar hona = high potential. Ek battery ek pump hai jo charge ko upar ek high point tak uthata hai; ek resistor ek slide hai jo charge ko wapas neecha girne deta hai, jaate waqt energy release karte hue. Deep version ke liye Electric Potential dekho.

"Difference" kyun, absolute height nahi? Sirf height ka fark hi cheezein move karata hai — jis actual sea-level se tum measure karo woh important nahi. Isliye circuits ko $V_{A} - V_{B}$ ki parwah hai, akele $V$ ki nahi.

6. EMF ( $ε$ ) — pump

$V$ se alag symbol kyun? Kyunki $ε$ energy ka ek source hai (ek rise jis par tum count kar sakte ho), jabki resistor ka $V$ ek drop hai jahan energy nikl jaati hai. Source ko uska khud ka letter dena KVL mein "rise vs drop" bookkeeping ko clean rakhta hai.

7. Resistance $R$ aur Ohm's Law — slide ki steepness

Padho: current $I$ jitna bada ya resistance $R$ jitna bada, voltage drop $V$ utni badi jitni tum use cross karte waqt kho dete ho. Yeh current ko voltage se jodne wala glue hai — Ohm's Law dekho. Kirchhoff's laws tumhe equations dete hain; Ohm's law unknown voltages ko unknown currents mein badalne deta hai taaki tum unhe actually solve kar sako.

Q

ka kya matlab hai, aur uska unit?

Electric charge — electric "stuff" ki miqdar; unit coulomb

C

I

ka kya matlab hai aur

Q

se kaise define hota hai?

Current — har second ek point se guzarne wala charge;

I = Δ Q /Δ t

, unit ampere

A

Δ

(delta) kya represent karta hai?

"Mein change" — baad wali value minus pehle wali value.

\frac{Δ Q}{Δ t}

ki jagah

\frac{d Q}{d t}

kyun likhte hain?

d

rate deta hai ek single instant par (tiny time slice), kisi chunk of time par average nahi.

Node kya hota hai?

Woh point jahan do ya zyada wires milti hain — ek junction. KCL yahan rehti hai.

Loop kya hota hai?

Koi bhi closed path jo apne start par wapas aaye. KVL yahan rehti hai.

Electric potential

V

kya hai, ek picture mein?

Ek point ki electrical "height"; charge high se low ki taraf flow karta hai jaise paani neecha.

Circuits ko potential ke differences kyun important hain, absolute potential kyun nahi?

Sirf height ka fark hi flow karata hai; reference level arbitrary hai.

ε

(EMF) kya hai aur uska unit?

Woh voltage jo battery supply karti hai (uski pump strength); unit volt

V

Ohm's law batao aur har letter kya hai.

V = I R

: resistor par voltage drop

V

current

I

times resistance

R

(ohms

Ω

) ke barabar hai.

\sum_{k} I_{k} = 0

words mein kya kehta hai?

Saare currents (signs ke saath, in

= +

, out

= -

) jodo aur total zero hai.

Node mein andar aane wale current aur bahar jaane wale current ko kaun sa sign dete hain?

Andar

= +

, bahar

= -

Connections

Ohm's Law — $V = I R$ supply karta hai, current aur voltage ke beech ka link.
Conservation of Charge — kyun $Q$ kabhi appear ya vanish nahi hota; KCL ki jad.
Conservation of Energy — kyun loop round-trip net zero deta hai; KVL ki jad.
Electric Potential — "electrical height" idea poori tarah se.
Series and Parallel Resistors — in foundations se bani pehli structures.
Mesh and Nodal Analysis — yahan assemble kiye gaye symbols ka systematic use.
Wheatstone Bridge — ek circuit jo is page ke har tool ko ek saath maangta hai.

Foundations — Kirchhoff's current law (KCL), Kirchhoff's voltage law (KVL)