You have a simple circuit: a 9V battery connected to a single resistor. The resistor is dissipating a certain amount of power as heat. Now you swap it out for a new resistor with TWICE the resistance, keeping the same 9V battery.
What happens to the power dissipated by the resistor?
The power drops to HALF! Here’s the trap: P = I²R suggests doubling R doubles power. But with a fixed voltage, the current also changes — I = V/R drops to half. So P = I²R = (V/2R)² × 2R = V²/2R. Use P = V²/R and it’s obvious: double R, half the power.
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Adjust the resistance slider and watch how current and power respond. Notice how V = IR plays out in real time — the voltage across the resistor stays at 9V, but the current and power change together.
V = IR
Three forms of power: P = IV = I²R = V²/R. Choose the form where you know the quantity that stays FIXED.
A 100W bulb has lower resistance than a 60W bulb. More current flows through it at the same voltage, so it glows brighter and hotter.
When resistance drops (short circuit), current spikes dramatically. Fuses melt and breakers trip to prevent fires — they’re Ohm’s law safety devices.
Fast chargers increase voltage (from 5V to 20V) to deliver more power without overheating the cable. P = V²/R means higher V is far more efficient.
Space heaters are just big resistors. They deliberately convert P = I²R watts of electrical energy into heat. A lower resistance coil means more current and more warmth.
“V = IR is the first equation of circuits, but P = IV is where the real story lives. Know what’s fixed, choose the right form, and circuits make sense.”
Circuit Builder
Build circuits with batteries, resistors, and wires. Watch current flow as electrons move through the circuit, and see how voltage, current, and power change in real time as you adjust resistance and voltage.
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Start with a single resistor and battery. Sweep the resistance from low to high and watch the current and power respond. Then try adding resistors in series — does the total resistance add up? Now try parallel — the result might surprise you. Watch the ammeter as you add more parallel paths for current to flow through.
Ohm’s law (V = IR) and the power equation (P = IV) together explain everything from why short circuits are dangerous to why power lines use high voltage. The key is always asking: what’s held constant?