OHM’S LAW
V = IR, and the power VI = I²R = V²/R — three routes to the same watt, all of it heat. Series adds, parallel divides, and R_series × R_parallel = R₁R₂ to the bit.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
Setup
A battery, a resistor, a wire — the whole of a first circuit. The voltage pushes; the resistance resists; the current that results is the negotiated settlement between them, and it costs energy to keep it flowing.
The law
Ohm’s law is a straight line: current is proportional to voltage, V = IR. Double the push, double the flow. The constant of proportionality is the resistance, and its reciprocal is the slope of the line — the defining behaviour of an ohmic conductor.
Solve
Put the numbers in and out comes the current — and, more quietly, the power. P = VI, and by Ohm’s law that is also I²R and V²/R: three roads to the same watt. Every one of those watts ends up as heat in the resistor.
Turn it up
Sweep the supply from zero. The operating point rides straight up the line, current climbing in lockstep, while the power — the shaded rectangle beneath it — grows as the square of the voltage. This is why a bulb glows brighter far faster than you turned it up.
Audit
Audited: the three power routes agree to the last bit, residual exactly zero; the line is ohmic to machine precision — doubling the voltage doubles the current bitwise; and the series/parallel identity R_series × R_parallel = R₁R₂ holds exactly.