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Ohm's law

Voltage = current × resistance. One equation, endless circuits.

first shows up at Level 1 · Light

Ohm's law is the one equation you'll use forever:

V = I × R

  • V — voltage, in volts. How hard the battery pushes.
  • I — current, in amps. How much electricity is actually flowing.
  • R — resistance, in ohms (Ω). How hard the part fights back.

Rearrange it for whichever piece you're solving for:

  • I = V ÷ R — "how much current will flow?"
  • R = V ÷ I — "what resistor do I need?"

Real example — picking an LED resistor

Every LED project on this site does the same calculation. Say you have a 4.5 V battery pack, a red LED that "eats" 2 V across itself, and you want about 10 mA through it:

  • Voltage left for the resistor: 4.5 V − 2 V = 2.5 V
  • Resistor size: R = 2.5 V ÷ 0.010 A = 250 Ω
  • Nearest common part: 220 Ω → real current ≈ 11 mA. Perfect.

That's it. Every "why 220? why not 470?" question has a real answer, and Ohm's law is how you get it. No guessing.

Projects that teach this

First Light Build a real flashlight circuit and learn why every circuit is a loop. L1 15 min Twin Reds Two red LEDs on one loop — same current, half the leftover push, and a lesson in how voltages stack when parts sit end to end. L1 15 min Escape Hatch The Vault with a big red emergency button wired around both locks — turn BOTH keys, or hit the button, and the light comes on. L1 20 min The Brightness Lab Run a real experiment: predict, measure with your eyes, and prove Ohm's law. L1 30 min Dial-a-Brightness Twist a knob and watch the LED fade up and down — your first "how much" input. L2 20 min Dial-a-Buzz Dial-a-Brightness for sound — one knob rides the buzzer between full alarm and library silence, with no button in the way. L2 15 min Continuity Tester Your first real tool — two probe wires that beep and light up whenever the tips touch anything that conducts. L2 20 min Whisper Alarm A doorbell with a volume knob — the pot lives in the buzzer lane, so twisting it changes the beep without touching the light. L2 25 min Two-Tone Doorbell Two call buttons, one doorbell: LOUD rings the buzzer and lights the porch LED; QUIET starves the buzzer and shows why it can't just be dimmed. L2 25 min Arm & Ring A doorbell that ignores you unless a hidden slide switch is armed first — series-AND with sound, plus an 'armed' LED that shows the state. L2 20 min Twin Bells One doorbell button rings two buzzers in parallel — one in your room, one in the kitchen — with a slide switch that mutes just the bedroom bell at night. L2 20 min Two-Hand Bell Two push buttons in series feeding a buzzer and an LED — both hands must stay pressed for the alarm to sound. L2 20 min Silent Alarm Three panic buttons wired in parallel, all inside an armed lane — any one of them fires the buzzer, and a small LED tells you the alarm is watching. L2 25 min Quiz Buzzer Two teams, two big buttons: yours lights your LED and rings your buzzer, theirs does the same on their side. Two independent doorbells sharing one battery. L2 20 min Automatic Night Light A light that switches itself on when the room gets dark — no hands, no code. L3 35 min Sunrise Alarm The night light — flipped. Swap two parts and the LED wakes up with the sun instead. L3 25 min Cookie Jar Alarm The Sunrise Alarm's brain wired to a buzzer instead of a lamp — quiet in the dark jar, screaming when the lid comes off. L3 25 min Trip Wire Alarm A thin wire across a doorway holds the alarm silent. Break the wire and the buzzer screams — until you connect it back. L3 25 min Warm Hand Alarm Cup your hand over the sensor and the LED lights up — a thermometer that turns into a switch. L3 30 min Reading Light The Automatic Night Light with a knob on top — turn it to dial in how dark the room has to get before the lamp fires. Your first tunable threshold. L3 30 min Vacation Nightlight The Automatic Night Light with a manual override — flip the slide switch off and the lamp stays dark even in a pitch-black room. L3 25 min Study Lamp The Automatic Night Light with a force-on override — flip the slide switch and the lamp stays lit even in daylight, ignoring the sensor. L3 25 min Curfew Beeper The Automatic Night Light's brain with a buzzer where the LED used to sit — beeps the moment the room goes dark, so you never miss sunset. L3 30 min Fever Beeper The Warm Hand Alarm's brain wired to a buzzer instead of a lamp — silent in a normal room, beeping the second a warm palm covers the sensor. L3 25 min Dusk Chorus The Curfew Beeper with a red LED wired in parallel with the buzzer — one dusk sensor drives a chime and a lamp at the same time. L3 30 min Warm Hand Chorus Fever Beeper with a red LED added in parallel with the buzzer — one warm-hand sensor drives a chime and a lamp at the same time. L3 30 min First Spin Your first motor. A switch, a coil, and a diode that catches the voltage kick when the current stops. L4 15 min Handheld Fan Press the button, the fan spins. A tiny finger current commands a hundred-milliamp motor through a transistor. L4 20 min Sunrise Fan Sunrise Alarm with the LED swapped for a motor. The sun rises, the fan starts — an automatic wake-you-up desk breeze. L4 25 min Panic Fan Two buttons, either one fires the fan. Panic Doorbell wearing a motor — an OR gate that spins. L4 20 min Party Spinner One button, three mouths: a spinning motor, a red LED, and a buzzer all fire together. One transistor drives them all. L4 25 min Twin Wheels Two motors from one button — a Level 9 robot drivetrain, five levels early. L4 25 min Dial-a-Spin Dial-a-Brightness with a motor instead of an LED. Twist the knob and watch the fan speed slide from full spin to a slow crawl. L4 20 min Trip Wire Fan Trip Wire Alarm's brain wearing a motor. The wire is intact — the fan is silent. Snap it — the fan spins as the alarm. L4 25 min

Parts you'll meet along the way

L1 1 kΩ resistorL1 10 kΩ resistorL1 220 Ω resistorL1 3×AA battery pack (4.5 V)L1 Green LED (5 mm)L1 Jumper wiresL1 Push button (tactile)L1 Red LED (5 mm)L1 Slide switchL1 Solderless breadboardL2 10 kΩ potentiometerL2 Active buzzer (3–5 V)L3 Light sensor (LDR)L3 NPN transistor (2N2222)L3 Temperature sensor (10 kΩ thermistor)L4 DC motor (3 V)L4 Diode (1N4001)