Apply Kirchhoff's Voltage Law (KVL) — Hinglish notes

1.2.4 · Hardware › Circuit Analysis Fundamentals

KVL HAI KYA?

YEH SACH KYUN HAI? (First principles se Derivation)

Do points ke beech voltage ko charge ko unke beech move karne ki work per unit charge ke roop mein define kiya jaata hai: $V_{A B} = \frac{W _{A B}}{q} = - \int_{A}^{B} E \cdot d l$

Iska matlab hai ki voltage (electric potential) ek conservative quantity hai — yeh sirf endpoints par depend karta hai, path par nahi.

Ab ek closed loop lo: point $A$ se shuru karo aur point $A$ par wapas aao. Endpoints ek hi point hain, isliye poore chakkar mein work per charge zero honi chahiye (ek conservative field closed path par net zero work karta hai): $\oint E \cdot d l = 0 ⟹ \sum_{k} V_{k} = 0$

(Caveat: yeh tab valid hai jab loop mein se koi changing magnetic flux na guzar raha ho. Agar time-varying $B$ -field ho, toh Faraday's law deta hai $\oint E \cdot d l = - d Φ_{B} / d t \neq = 0$ . Standard lumped DC/low-frequency circuits ke liye, KVL hold karta hai.)

ISKO APPLY KAISE KAREIN — sign convention (woh part jahan sabse zyada galti hoti hai)

Figure — Apply Kirchhoff's Voltage Law (KVL)

Worked Example 1 — Single loop, ek source

Ek $12 V$ battery current ko do series resistors $R_{1} = 4 Ω$ aur $R_{2} = 2 Ω$ se guzarti hai. Current $I$ nikalo.

Worked Example 2 — Do sources opposing

Loop mein ek $10 V$ source, ek $4 V$ source opposing hai, aur ek resistor $R = 3 Ω$ hai. $I$ nikalo.

Worked Example 3 — Known answer se Verify karo (Forecast-then-Verify)

Series: $9$ V source, $R_{1} = 3 Ω$ , $R_{2} = 6 Ω$ . Forecast: total $R = 9 Ω$ , toh $I = 1$ A; drops $3$ V aur $6$ V.

Classic mistakes ko Steel-man karna

Active Recall

Recall KVL ko ek 12-saal ke bachche ko explain karo (Feynman)

Voltage jaisa ki tum kitne upar ho. Battery ek escalator hai jo tumhe upar uthati hai; resistor ek slide hai jo tumhe neeche laata hai. Agar tum poora chakkar lagao aur wapas shuru wali jagah aao, toh tumhe same height par hona chahiye — toh saare ups aur downs cancel out hokar zero ho jaate hain. Yahi KVL hai!

KVL ek closed loop ke baare mein kya kehta hai?

Kisi bhi closed loop mein saare voltages ka algebraic sum zero hota hai.

KVL ko sach banane wala physical principle kya hai?

Electric potential conservative hai — ek closed path same potential par wapas aata hai, toh net voltage change zero hota hai.

KVL kab fail ho sakta hai?

Jab loop mein se time-varying magnetic flux guzarta hai (Faraday's law), jo nonzero loop EMF deta hai.

Agar tumhara assumed current negative aaye, toh uska kya matlab hai?

Actual current opposite direction mein flow kar raha hai; magnitude phir bhi sahi hai.

Jab kisi element ko traverse karte waqt uske

+

terminal se exit karo toh sign rule kya hai?

Ise voltage rise likho,

+ V

Resistor mein voltage drop kis direction mein hota hai?

Current ki direction mein (current

+

terminal se enter karta hai).

Example 1 mein (12 V, 4 Ω, 2 Ω series), current kya hai?

I = 2

Kya traversal direction badalne se answer change hota hai?

Nahi — yeh sirf poori equation ko

- 1

se multiply karta hai; solution identical hota hai.

Connections

Kirchhoff's Current Law (KCL) — companion law (nodes par charge conservation).
Ohm's Law — KVL equations ke andar $V$ ko $I R$ mein turn karne ke liye use hota hai.
Voltage Divider — series loop mein KVL ka direct consequence.
Conservation of Energy — KVL energy conservation per unit charge hai.
Mesh Analysis — multiple loops par KVL ka systematic application.
Faraday's Law — "no changing flux" caveat ki wajah.