1.2.3
Intuition Ek-sentence wala ideaEk circuit node bilkul plumbing junction jaisa hai: jo paani andar aata hai woh bahar bhi jaana chahiye — charge kisi point par ikatta ho sakta hai na gayab ho sakta hai, isliye node mein enter karne wale currents ka sum, bahar jaane wale currents ke sum ke barabar hota hai .
Definition Kirchhoff's Current LawKisi bhi node par (ek junction jahan 2 ya zyada wires milti hain), sabhi currents ka algebraic sum zero hota hai:
∑ k i k = 0 ∑ i in = ∑ i out node = koi bhi point jo sirf ideal wires (zero resistance) se connected ho. Ek hi wire par saare points ek hi node hote hain.
WHY yeh exist karta hai? KCL bas conservation of electric charge ka ek point par application hai. Ek node mein charge store karne ki koi capacitance nahi hoti, isliye har instant par charge in = charge out.
Charge conserved hota hai. Ek choti si region (node) ke andar stored charge Q ( t ) i = d t d q
Continuity statement: charge ke accumulate hone ki rate = (andar aane ki rate) − (bahar jaane ki rate):
d t d Q node = ∑ i in − ∑ i out
Ek ideal node charge store nahi kar sakta (Q node = 0 d t d Q = 0 ∑ i in − ∑ i out = 0 ⟹ ∑ i in = ∑ i out
Intuition "Algebraic sum = 0" kyun?Agar hum ek sign convention adopt karein — maan lo currents jo leave kar rahe hain positive hain , enter karne wale negative hain — toh "in = out" ek clean equation ∑ i k = 0
Worked example Example 1 — Simple 3-wire junctionCurrents i 1 = 3 A i 2 = 2 A flow in karte hain. Ek current i 3 flow out karta hai. i 3
Step 1 — KCL likho (in = out).
Yeh step kyun? Koi charge accumulate nahi hota, isliye jo bhi andar aaya woh bahar jaana chahiye.
i 1 + i 2 = i 3 Step 2 — Substitute karo.
3 + 2 = i 3 ⇒ i 3 = 5 A Kyun: Akele outgoing wire ko poora incoming charge flow carry karna hoga.
Worked example Example 2 — Char branches with unknownNode B par: i 1 = 4 A i 2 = 6 A i 3 = 7 A i 4 = ?
Step 1 — Sum in = sum out.
Kyun: conservation.
i 1 + i 2 = i 3 + i 4 Step 2 — Solve karo.
4 + 6 = 7 + i 4 ⇒ i 4 = 3 A (out) Kyun: 10 7 i 3 3 i 4
Worked example Example 3 — Galat guess direction (self-correction)Node C par, known: 5 A 2 A guess kiya ki i x in flow karta hai. Convention use karo "leaving = +", aur ek branch mein 8 A
Step 1 — ∑ i leave = 0
Enter karne wale currents negative count hote hain:
− 5 − 2 − i x + 8 = 0 Step 2 — Solve karo.
i x = 1 A Positive answer kyun theek hai: i x = + 1 math apne aap guess self-correct kar leta hai.
Worked example Example 4 — Node with a current sourceEk 10 A i 1 i 2 i 1 = 6 A i 2
Step 1 — KCL. 10 = i 1 + i 2 Step 2. i 2 = 10 − 6 = 4 A Kyun: source current poori tarah exits mein distribute ho jaata hai; kuch bhi lost nahi hota.
Common mistake "Main direction ki parwah kiye bina magnitudes add kar lunga."Kyun sahi lagta hai: currents "amounts" hain, aur amounts add karna natural lagta hai.
Kyun galat hai: direction physical hai — ek incoming aur outgoing current subtract hote hain, add nahi hote.
Fix: hamesha arrows + signs assign karo; entering aur leaving ke opposite signs hote hain.
Common mistake "Ek hi wire par do resistors = do nodes."Kyun sahi lagta hai: woh dekhne mein alag components lagte hain.
Kyun galat hai: ideal wire mein koi voltage drop nahi hota; uska har point electrically identical hota hai — ek node .
Fix: KCL likhne se pehle pure wire se joined saare points ko ek single node mein collapse karo.
Common mistake "Ek capacitor KCL violate karta hai kyunki charge uski plates par store hota hai."Kyun sahi lagta hai: capacitors literally charge store karte hain.
Kyun galat hai: charge component ke andar plates par store hota hai, node par nahi. Current i = C d v / d t Fix: capacitor terminal current ko kisi bhi branch current ki tarah treat karo.
Recall Feynman: ek 12-saal ke bachche ko explain karoSocho ek road roundabout jahan gaadiyaan enter aur leave karti hain. Gaadiyaan roundabout par magically gayab ya spawn nahi ho saktiN — isliye jo gaadiyaan per minute andar aa rahi hain unki sankhya, bahar jaane wali gaadiyon ki sankhya ke barabar honi chahiye. Electric current bas charges (tiny cars) hain jo wires mein move karte hain. Wires ke kisi bhi junction par, jo bhi charge andar aaye woh bahar bhi jaana chahiye. Yahi KCL hai!
"In = Out, Charge Can't Sprout." Node par kuch bhi create ya destroy nahi hota.
Answers cover karo. KCL do tareekon se batao. Ek ideal node par charge kyun accumulate nahi ho sakta? Ek negative computed current ka kya matlab hai?
Kirchhoff's Current Law (algebraic form) batao. Kisi bhi node par currents ka algebraic sum zero hota hai: ∑ i k = 0
KCL seedha kis conservation law ka consequence hai? Conservation of electric charge.
Ek ideal node ∑ i in = ∑ i o u t Ek ideal node koi charge store nahi karta, isliye d Q / d t = 0
Circuit analysis mein "node" kya hota hai? Do ya zyada branches ka ek junction; ideal (zero-resistance) wire se connected saare points ek hi node banate hain.
Agar tum kisi current ki direction galat guess karo, toh solve karne par kya hoga? Tumhe ek negative value milegi; uska magnitude sahi hoga aur tum bas assumed arrow reverse kar do.
Kya ek continuous wire par do components ek node banate hain ya do? Ek node — ideal wire mein koi voltage drop nahi hota, isliye yeh sab ek hi electrical point hai.
Kya ek capacitor KCL violate karta hai? Nahi — terminal current i = C d v / d t
3 A aur 2 A ek node mein enter karte hain; ek wire bahar jaati hai. Kaunsa current bahar jaata hai? 5 A.
Kirchhoff's Voltage Law (KVL) — voltage counterpart (ek loop ke around energy conservation).Nodal Analysis — systematically har node par KCL apply karta hai poore circuits solve karne ke liye.Conservation of Charge — KCL ki physical foundation.Current and Current Density — i = d q / d t Ideal Wires and Nodes — kyun same-wire points ek node hote hain.Capacitor i-v Relationship — capacitor "storage" misconception clarify karta hai.
Ideal node stores no charge
