Circuit: A 12 V source and a 3 A source share a node. R1=4Ω connects the 12 V source to node A; R2=6Ω connects node A to ground; the 3 A source pushes current into node A. Find VA.
Contribution of the 12 V source (kill 3 A → open):VA,1=12⋅R1+R2R2=12⋅106=7.2 VWhy this step? With the current source open, R1 and R2 form a simple voltage divider from 12 V to ground.
Contribution of the 3 A source (kill 12 V → short):
With 12 V shorted, R1 and R2 are both from node A to ground → they're in parallel:
R1∥R2=4+64⋅6=2.4Ω,VA,2=3×2.4=7.2 VWhy this step? All 3 A flows out of node A through the parallel resistance to ground, so V=IR∥.
Same circuit, node equation at A (currents leaving = 0):
4VA−12+6VA−3=0Why this step? KCL: current toward the 12 V source + current to ground − injected 3 A = 0.
Multiply by 12: 3(VA−12)+2VA−36=0⇒5VA=72⇒VA=14.4 V ✓
Superposition and nodal analysis agree — as linearity guarantees.
Imagine a swimming pool with two hoses filling it. If you want to know the water level, you can figure out how much hose A alone raises it, then how much hose B alone raises it, and just add. That works because water levels just add up. Circuits with resistors are the same: each battery or current-pump raises voltages by its own amount, and you add the amounts. BUT if you tried to add up "splashiness" (which grows with the square of flow), it wouldn't work — because squaring isn't just adding. That squaring thing is why we never add up power directly.
Superposition theorem ka core idea simple hai: agar circuit linear hai (sirf resistors, ideal sources, koi diode ya squaring nahi), aur usme kai independent sources hain, to kisi bhi point ka voltage ya current nikalne ke liye tum ek-ek source ko alag-alag on karke answer nikaalo, aur phir sabko add kar do. Kyun kaam karta hai? Kyunki Kirchhoff ke laws aur Ohm ka law sab linear equations hain, aur linear equations me inputs ka sum ka jawab, alag-alag jawabon ka sum hota hai.
Jab ek source ko "off" karte ho to yaad rakho: voltage source ko short kar do (0 V matlab seedha taar), aur current source ko open kar do (0 A matlab gap). Mnemonic: "V-Short, I-Open". Dependent sources ko kabhi off mat karo — wo circuit ke variables pe depend karte hain, isliye har step me active rehte hain.
Example me humne 12V source aur 3A source ka contribution alag-alag nikaala: 12V se voltage divider se 7.2 V mila, aur 3A se parallel resistance ke through 7.2 V mila. Add karke 14.4 V — aur nodal analysis se bhi exactly wahi aaya. Yeh confidence deta hai ki method sahi hai.
Sabse bada trap: power ko superpose mat karo! Power i2R hai, yaani square wala nonlinear cheez — (i1+i2)2=i12+i22. Pehle currents ya voltages add karo, total nikaalo, phir ek hi baar power compute karo. Yeh chota sa dhyan exam me bade marks bachaata hai.
