Use Norton equivalent circuits — Hinglish notes

1.2.10 · Hardware › Circuit Analysis Fundamentals

Norton equivalent exist kyun karta hai?

Woh do numbers kya hain?

Norton equivalent kaise nikalein (recipe)

Worked Example 1 — ek real network

Worked example Do resistors aur ek source

Ek $12 V$ source $R_{1} = 4 Ω$ ko series mein feed karta hai ek node tak; us node se $R_{2} = 6 Ω$ bottom rail tak jaata hai. Output terminals $R_{2}$ ke across hain. Norton equivalent nikalo.

Step 1 ( $I_{N}$ ): Output terminals ko short karo. Yeh $R_{2}$ ko short kar deta hai (uske dono ends ab jud gaye), toh saari current short se jaati hai: $I_{N} = \frac{12}{4} = 3 A .$ Kyun? Short ke saath, $R_{2}$ par koi voltage nahi, toh woh invisible hai; sirf $R_{1}$ source ko limit karta hai.

Step 2 ( $R_{N}$ ): Source ko kill karo (12 V → wire). Ab $R_{1}$ aur $R_{2}$ dono terminals ko connect karte hain — woh parallel mein hain: $R_{N} = \frac{4 \cdot 6}{4 + 6} = 2.4 Ω.$ Parallel kyun? Source deactivate karne se $R_{1}$ aur $R_{2}$ ke tops aapas mein jud jaate hain aur terminals $R_{2}$ ke across hain, toh dono resistors same do nodes bridge karte hain.

Result: $I_{N} = 3 A ∥ R_{N} = 2.4 Ω$ .

Worked Example 2 — use karke load solve karo

Norton ↔ Thévenin (same line, do descriptions)

Common mistakes

Recall Feynman: ek 12-saal ke bachche ko samjhao

Socho ek water tank pipes se tumhare sink ko feed karta hai. Har pipe draw karne ki jagah, main tumhe ek card deta hoon: "yeh tap 3 cups per second dhakelta hai, aur ek leaky pipe hai 'thickness 2.4' ki jo kuch chura leti hai." Ab tum predict kar sakte ho kitna paani kisi bhi cup tak pahunche ga — tank dobara dekhe bina. Norton = circuit ke outlet ka sabse chhota imeandaar summary.

Flashcards

Ek linear two-terminal network ka Norton equivalent kya hota hai?

Ek current source

I_{N}

in parallel with a resistance

R_{N}

Norton current

I_{N}

kaise nikalte hain?

Output terminals short karo aur short se guzarne wali current compute karo.

Norton resistance

R_{N}

kaise nikalte hain?

Saare independent sources deactivate karo (V→short, I→open) aur terminals ke beech resistance nikalo.

Norton terminal equation kya hai?

I_{L} = I_{N} - V / R_{N}

R_{N}

aur

R_{T h}

mein kya relation hai?

Dono equal hain:

R_{N} = R_{T h}

Thévenin ko Norton mein convert karo.

I_{N} = V_{T h} / R_{T h}

, aur

R_{N} = R_{T h}

Linear network ke liye terminal I–V relationship straight line kyun hoti hai?

Superposition/linearity

I

V

ka affine function banati hai:

I = aV + b

, jo sirf do parameters maangti hai.

I_{N}

nikalte waqt terminals ke across resistor ko ignore kyun kiya ja sakta hai?

Parallel mein short saari current le jaata hai, toh us par 0 V hota hai aur woh invisible ho jaata hai.

Norton source se load

R_{L}

mein current-divider?

I_{L} = I_{N} \cdot R_{N} / (R_{N} + R_{L})

Connections

Thévenin equivalent circuits — voltage-source twin; freely convert karo.
Source transformation — bridge $V_{T h} = I_{N} R_{N}$ .
Ohm's Law — $V / R_{N}$ leak term provide karta hai.
Kirchhoff's Current Law — node par $I_{L} = I_{N} - V / R_{N}$ justify karta hai.
Maximum power transfer — max load power ke liye $R_{L} = R_{N}$ use karta hai.
Superposition — kyun terminal behavior linear/affine hai.