how circuits work

voltage is the push, current is the flow, resistance is the friction. capacitors store charge, inductors store magnetic energy, diodes set direction, and transistors control bigger things with smaller signals.

ohm sweet ohm (and friends)

• ohm’s law: V = I × R, I = V / R, R = V / I
• power: P = V × I = I²R = V²/R (watch part wattage)
• kirchhoff: currents into a node sum to 0; voltages around a loop sum to 0.

voltage divider

two resistors make a reference voltage.

Vout = Vin × R2 / (R1 + R2)

example: Vin = 9 V, R1 = 10 kΩ, R2 = 10 kΩ → Vout = 4.5 V.

filters (rc)

one resistor + one capacitor make simple “tone controls.”

• low-pass (smooths): cutoff fc = 1 / (2πRC)
• high-pass (blocks dc): same formula, parts swapped

example: R = 10 kΩ, C = 1 µF → f_c ≈ 15.9 Hz (great for de-bouncing).

diodes + leds

• forward drop: ~0.7 V (silicon), ~0.2 V (schottky), LED ~2.0–3.2 V depending on color.
• series resistor for leds: R = (Vsupply − Vf)/I.
• flyback diode: across coils (stripe to +) to catch the spike.

transistors (super quick)

• npn low-side switch: base via ~1 kΩ, emitter to ground, collector to load → +V. add diode for motors/relays.
• logic-level n-mosfet: gate ~0–5 V via 100 Ω, 100 kΩ pulldown to gnd; drain to load; source to gnd.

stable power

• decouple every ic with 0.1 µF right at the power pins + 10–47 µF bulk per rail.
• mind current: usb is typically 500 mA (2.0), 900 mA (3.0), or more if negotiated; don’t assume unlimited.
• ground is your friend: keep returns short; use a ground plane on pcbs.

reading schematics

• follow the power path first (battery/regulator → decoupling → chips).
• look for sub-circuits: input conditioning, brain (logic/mcu), output drivers.
• unused inputs? tie them high or low; don’t float cmos gates.
• label nets (VCC, LED_A, SCL) so the diagram reads like a story.