Electrical & Electronics
The math behind circuits, wiring, and electronics
10 live exhibits. Each one already works. Change a number and see what happens.
Open as board Play with these together. Solving one grows related exhibits.
Linear EquationsOhm’s law: how much current flows?
Push harder (volts) or squeeze tighter (ohms), and watch the current change.
Linear EquationsHow many amps does it draw?
Watts divided by volts gives amps. That decides the breaker and the wire.
Ratios & ProportionsWire resistance: longer and thinner resist more
Resistance grows with length and shrinks with thickness. Pick the wire that keeps it low.
Linear EquationsVoltage drop: what the wire takes before the load gets it
Current times wire resistance is voltage you never get to use.
Linear EquationsVoltage divider: two resistors make a new voltage
The output is the input times a ratio of resistors, until you connect a load.
Linear EquationsPC cooling: passive, air, or water?
Heat flows through the cooler like current through a resistor: temperature rise = watts × °C/W. Water adds mass, so it heats up slower.
TrigonometrySine waves: wall power and musical notes
The outlet and a tuning fork follow the same curve: amplitude, frequency, and phase.
Linear EquationsDC motor torque–speed curve: where it runs, peaks, and stalls
Load a DC motor and its speed falls in a straight line to stall. Power peaks at half speed, and efficiency peaks at light load.
PolynomialsWhy a distortion pedal changes the sound: polynomials make harmonics
Push a pure note through a curve like x − x³/3 and new notes appear. The cube is where the extra harmonics come from.
VectorsSolar panel tilt: how much sunlight it catches
Point one arrow at the sun and one straight out of the panel. Their dot product is the share of full sunlight the panel gets.