Intuition The one core ideaA circuit built only from parts that respond in strict proportion to what you feed them lets you study each power source one at a time and simply add up the separate answers. This page builds — from nothing — every word and symbol you need before that adding-up trick (superposition) can make sense.
Below, each item is: plain words → the picture → why the topic needs it. They are ordered so each one leans only on the ones above it. Nothing is used before it is built.
Before any symbols, look at the map of a tiny circuit. A circuit is just loops of wire with components sitting in the wire, and sources that push energy in. Everything else on this page is a label we hang on parts of this picture.
The tall battery-looking symbol on the left is a voltage source .
The circle with an arrow on the right is a current source .
The zig-zag boxes are resistors .
The flat line at the bottom is ground — our agreed "sea level".
The dot labelled A node .
We now define every one of those words.
Voltage is the difference in electrical height between two points. Symbol: v V volt , written V
Intuition The picture: height on a hillImagine two points on a hillside. Voltage is the drop in height between them. A ball (charge) at a higher point wants to roll down; the bigger the height difference, the harder it is pushed. Voltage is always between two points — asking "the voltage at one point" only makes sense once we agree where "the ground" is (see item 3).
Why the topic needs it: superposition finds a voltage (like V A
Current is the rate of flow of charge through a wire — how much charge passes a point each second. Symbol: i I ampere , written A
Intuition The picture: water in a pipeIf voltage is height difference, current is the litres-per-second of water actually moving through a pipe. A steeper drop (more voltage) tends to push more flow (more current), but the pipe's narrowness (resistance, item 4) limits it.
Why the topic needs it: the other thing superposition adds up is current (like I R 2
Common mistake "Voltage flows through the resistor."Why it feels right: we say "current flows", so voltage sounds like it flows too. Why it's WRONG: voltage is across two points (a difference); current is through a component (a flow). Fix: across = voltage, through = current. Always.
Ground is the one point we declare to be 0 V relative to ground ".
A node is any point where two or more wire ends join. Along a single unbroken wire, every point is the same node (same voltage), because ideal wire has no drop across it.
In the figure, points connected by plain wire share one colour — they are the same node and hence the same voltage . The parent's target V A A
Why the topic needs it: "V A merges two nodes into one voltage .
Resistance measures how much a component opposes current for a given voltage across it. Symbol: R ohm , written Ω
Intuition Why this exact shape mattersRead v = R i straight line through the origin : double the current, exactly double the voltage. No current → no voltage. This strict proportionality is what the word **linear** means. Superposition lives or dies on this line staying straight.
Why we chose a line and not a curve: if the graph bent (like a diode's), then feeding in "input A plus input B" would not give "answer A plus answer B" — the curve would double-count the bend. A straight line is the only shape where separate pushes add cleanly. That is the whole reason superposition is allowed.
Why the topic needs it: every resistor relation in the parent (V A , 1 = 12 ⋅ R 1 + R 2 R 2 V = I R ∥
Definition Series and parallelTwo resistors are in series if the same current must pass through both, one after the other. They are in parallel if they connect the same two nodes , so they share the same voltage .
Intuition Why the divider looks like thatThe same current i = R 1 + R 2 V R 2 i R 2 V ⋅ R 1 + R 2 R 2 R 2 share of the total resistance. Bigger share of the resistance → bigger share of the voltage.
Why the topic needs it: the parent's very first line, 12 ⋅ 10 6 = 7.2 is the voltage divider. See Voltage divider and current divider .
KCL (Kirchhoff's Current Law): at any node, currents flowing in equal currents flowing out (charge does not pile up).KVL (Kirchhoff's Voltage Law): around any closed loop, the voltage rises and drops sum to zero (you end at the same height you started).
Intuition Both are just "sums = 0"KCL says ∑ i = 0 ∑ v = 0 linear equations — plain sums, no squares, no products. That linearity, stacked on Ohm's linear v = R i exactly what makes the add-up trick provable.
Why the topic needs it: the parent's check "4 V A − 12 + 6 V A − 3 = 0 A Kirchhoff's Voltage and Current Laws and Nodal and mesh analysis .
Definition Independent sourceAn independent source sets its voltage (or current) to a fixed value by itself , no matter what the rest of the circuit does. The 12 V 3 A
Definition Dependent sourceA dependent (controlled) source sets its value as a formula of some other voltage or current in the circuit . It is a follower, not a leader.
Common mistake "Switch off dependent sources too."Why it feels right: they are still called "sources". Why it's WRONG: they encode real physics that depends on the circuit; killing them deletes that physics. Fix: only independent sources are toggled on/off during superposition.
Why the topic needs it: the entire recipe is "activate ONE independent source, kill the other independent ones." You must be able to tell the two apart.
Definition Short and open
A short circuit is a plain wire: it forces the two ends to the same voltage (v = 0 any current.
An open circuit is a gap: it forces zero current through it, while allowing any voltage across it.
Intuition Why kill V with a short, I with an openA voltage source fixes voltage . Set that fixed voltage to zero and you have "0 V across it" — which is precisely a wire (short) . A current source fixes current . Set that fixed current to zero and you have "no path" — precisely a gap (open) . Each dead source becomes the thing that naturally represents its own zero.
Voltage → Short, Current → Open. "Very Silly Idea? Open up!"
Why the topic needs it: step 1 of the recipe is literally replacing dead sources with shorts and opens.
An algebraic sum adds numbers with their signs — contributions in opposite directions partly cancel. A contribution of + 1.2 A − 0.5 A + 0.7 A 1.7
Intuition Why signs, not magnitudesEach source pushes current in some direction. Before you start, you pick a reference arrow for the target. A push with the arrow counts positive; against it, negative. Add the signed pieces and you get the true total.
Why the topic needs it: step 4 of the recipe says "add algebraically , respecting polarity." Getting a sign wrong is the classic superposition error.
Intuition The square breaks the straight lineVoltage and current follow straight lines, so they add. Power has an i 2 curve . And ( i 1 + i 2 ) 2 = i 1 2 + 2 i 1 i 2 + i 2 2 = i 1 2 + i 2 2 2 i 1 i 2 never superpose power. Add currents first, get the total, then square once. See Why power does not superpose .
Voltage v across two points
Divider and series parallel
Independent vs dependent sources
Kill sources V short I open
Power i squared R nonlinear
Cover the right side and test yourself.
What does voltage measure, and between how many points? The electrical "height" difference — always between two points (relative to ground).
What does current measure, and through what? The flow rate of charge through a wire or component.
State Ohm's law and say why its straight-line shape matters. v = R i
What is a node, and what is true of all points on one node? A junction of wires; every point on the same node has the same voltage .
What is ground? The point we declare to be 0 V
Voltage divider: fraction of V R 2 R 1 V ⋅ R 1 + R 2 R 2
Parallel resistance of R 1 R 2 R 1 + R 2 R 1 R 2
State KCL and KVL in one word each about "sums". KCL: node currents sum to zero; KVL: loop voltages sum to zero.
Difference between independent and dependent sources? Independent sets its value by itself; dependent sets its value from another circuit variable.
How do you kill a voltage source? A current source? V → short (wire); I → open (gap). "V-Short, I-Open".
Which sources are never killed in superposition? Dependent (controlled) sources — they always stay active.
Why can't power be superposed? P = i 2 R 2 i 1 i 2 ( i 1 + i 2 ) 2 = i 1 2 + i 2 2
1.2.11 Apply superposition theorem (Hinglish) 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