Apply superposition theorem — Hinglish notes

1.2.11 · Hardware › Circuit Analysis Fundamentals

Superposition KYUN kaam karta hai?

Yehi wajah hai ki yeh kisi bhi nonlinear cheez ke liye fail karta hai (diodes, transistors generally, power $= i^{2} R$ ).

"Source switch off karna" MATLAB kya hota hai?

Ise KAISE apply karein — recipe

Worked Example 1 — ek voltage + ek current source

Circuit: Ek $12 V$ source aur ek $3 A$ source ek node share karte hain. $R_{1} = 4 Ω$ 12 V source ko node $A$ se connect karta hai; $R_{2} = 6 Ω$ node $A$ ko ground se connect karta hai; 3 A source current into node $A$ push karta hai. $V_{A}$ find karo.

12 V source ka contribution (3 A kill → open): $V_{A, 1} = 12 \cdot \frac{R _{2}}{R _{1} + R _{2}} = 12 \cdot \frac{6}{10} = 7.2 V$ Yeh step kyun? Current source open hone par, $R_{1}$ aur $R_{2}$ 12 V se ground tak ek simple voltage divider banate hain.

3 A source ka contribution (12 V kill → short): 12 V short hone par, $R_{1}$ aur $R_{2}$ dono node $A$ se ground tak hain → yeh parallel mein hain: $R_{1} ∥ R_{2} = \frac{4 \cdot 6}{4 + 6} = 2.4 Ω, V_{A, 2} = 3 \times 2.4 = 7.2 V$ Yeh step kyun? Saara 3 A node $A$ se parallel resistance ke through ground mein flow karta hai, isliye $V = I R_{∥}$ .

Add karo: $V_{A} = 7.2 + 7.2 = 14.4 V$

Worked Example 2 — direct nodal analysis se check karo

Same circuit, node $A$ par node equation (currents leaving = 0): $\frac{V _{A} - 12}{4} + \frac{V _{A}}{6} - 3 = 0$ Yeh step kyun? KCL: 12 V source ki taraf current + ground ki taraf current − inject hua 3 A = 0.

12 se multiply karo: $3 (V_{A} - 12) + 2 V_{A} - 36 = 0 \Rightarrow 5 V_{A} = 72 \Rightarrow V_{A} = 14.4 V$ ✓

Superposition aur nodal analysis agree karte hain — jaisa ki linearity guarantee karti hai.

Worked Example 3 — ek current jo humein chahiye

Example 1 mein $R_{2}$ ke through current $I$ (neeche, ground ki taraf) find karo.

Sirf 12 V se: $I_{1} = V_{A, 1} / R_{2} = 7.2/6 = 1.2 A$ .
Sirf 3 A se: $I_{2} = V_{A, 2} / R_{2} = 7.2/6 = 1.2 A$ .
Total: $I = 1.2 + 1.2 = 2.4 A$ . Check: $V_{A} / R_{2} = 14.4/6 = 2.4$ ✓

Common mistakes (Inhe samajhkar steel-man karo)

Recall Feynman: ek 12-saal ke bachche ko samjhao

Ek swimming pool imagine karo jisme do hoses paani bhар rahi hain. Agar tum paani ka level jaanna chahte ho, tum figure out kar sakte ho ki sirf hose A kitna level badhata hai, phir sirf hose B kitna badhata hai, aur bas add kar do. Yeh isliye kaam karta hai kyunki water levels seedha add ho jaate hain. Resistors wale circuits waise hi hain: har battery ya current-pump voltage ko apni taraf se badhata hai, aur tum amounts add kar dete ho. LEKIN agar tum "splashiness" (jo flow ke square ke saath badhti hai) add karne ki koshish karo, toh kaam nahi karega — kyunki squaring sirf adding nahi hoti. Wahi squaring wali baat hai jis wajah se hum kabhi directly power add nahi karte.

Flashcards

Superposition theorem statement

Ek linear circuit mein, kisi bhi point ka response = har ek independent source ke akele kaam karne se aane wale responses ka algebraic sum (baaki killed).

Superposition kyun kaam karta hai?

Kirchhoff's laws + linear element relations linear equations banate hain; inputs ke sums ke solutions, solutions ke sums ke barabar hote hain.

Ideal voltage source ko kill kaise karein

Short circuit se replace karo (0 V = wire).

Ideal current source ko kill kaise karein

Open circuit se replace karo (0 A = gap).

Kya dependent sources superposition mein deactivate hote hain?

Nahi — yeh circuit variables par depend karte hain aur har sub-analysis mein active rehna chahiye.

Kya power superposition se find hoti hai?

Nahi — power (

i^{2} R

) nonlinear hai; pehle currents/voltages superpose karo, phir power compute karo.

Sources kill karne ka mnemonic

"V-Short, I-Open".

Example: divider 12V across 4Ω phir 6Ω to ground, node par V?

12 \cdot 6/10 = 7.2

Superposition result ko combine kaise karein?

Algebraically add karo, har contribution ki sign/polarity respect karte hue.

Connections

Linearity and homogeneity
Kirchhoff's Voltage and Current Laws
Voltage divider and current divider
Thevenin and Norton equivalents
Nodal and mesh analysis
Why power does not superpose