Physics Fundamentals

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Connect components to hit target voltages.
Real nodal analysis. 5 levels of circuit puzzles.

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⚡ Electromagnetism Game

Circuit Builder — Free Online Ohm's Law & Circuit Puzzle Game

Circuit Builder uses real nodal analysis — the same mathematical technique used by SPICE circuit simulators — to calculate voltages. Click nodes to connect components and watch live voltage readouts appear across every node and component in the circuit.

The physics behind the game

Ohm's law

V = IR

The fundamental relationship between voltage, current and resistance. Double the voltage, double the current. Double the resistance, halve the current.

Series resistors

R_total = R₁ + R₂ + R₃…

In series, all current flows through each component. Resistances add. Voltage divides proportionally to resistance.

Parallel resistors

1/R_total = 1/R₁ + 1/R₂

In parallel, current splits between paths. Total resistance is less than either individual resistor. Both components see the same voltage.

Kirchhoff's laws

ΣV_loop = 0, ΣI_node = 0

KVL: voltages around any loop sum to zero (energy conservation). KCL: currents into any node sum to zero (charge conservation). These underpin all circuit analysis.

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Circuits, Ohm's Law, and Kirchhoff's Rules

Ohm's Law: V = IR

For an ohmic resistor at constant temperature, voltage and current are proportional: V = IR (R in ohms). Power dissipated: P = IV = I²R = V²/R. Series resistors: R_total = R₁ + R₂ + … (same current, voltage divides). Parallel: 1/R_total = 1/R₁ + 1/R₂ + … (same voltage, current divides). Parallel resistance is always less than the smallest individual resistor.

Kirchhoff's Laws

KCL (Current Law): sum of currents at any junction = 0 (conservation of charge). KVL (Voltage Law): sum of voltages around any closed loop = 0 (conservation of energy). With V = IR, KCL and KVL give a complete system of equations solvable for any circuit's unknown currents and voltages. Nodal analysis (applying KCL to each node) is the standard systematic method.

Internal Resistance

Real batteries have internal resistance r. Terminal voltage V_term = EMF − Ir. Under heavy load (large I), terminal voltage drops significantly. A 9V battery with r = 2 Ω delivering 1 A: V_term = 9 − 1 × 2 = 7 V. Under short circuit (R_load = 0): I = EMF/r — potentially damaging. This is why batteries heat up under load and why car batteries can't start a car when deeply discharged.

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