Ohm's Law

One equation runs all of basic electronics:

V = I × R

Voltage = Current × Resistance. Know any two, get the third. That's it — everything else in this chapter is that sentence wearing different clothes.

The three arrangements

You know	You want	Formula
V and R	Current	I = V / R
I and R	Voltage	V = I × R
V and I	Resistance	R = V / I

Worked example: 5V across a 220Ω resistor. Current?

I = V / R = 5 / 220 = 0.0227 A = 22.7 mA

Check (verified): 22.7 mA. (Milliamps — a thousandth of an amp. Electronics lives in mA the way cooking lives in teaspoons.)

Power: the heat equation

Current through resistance makes heat. How much:

P = V × I

Power in watts. This tells you whether a component survives:

Worked example: that 220Ω resistor with 22.7 mA through it:

P = 5 V × 0.0227 A = 0.114 W

Check (verified): 0.114 W — well under a standard ¼ W (0.25 W) resistor's rating. If the math said 0.5 W, you'd need a bigger resistor — undersized resistors overheat, discolor, and fail.

Series and parallel

Series (one path, components in a line):

R_total = R1 + R2          →  220Ω + 220Ω = 440Ω

Same current everywhere; voltage divides across components.

Parallel (multiple paths):

1/R_total = 1/R1 + 1/R2    →  1/220 + 1/220 → R_total = 110Ω

Same voltage everywhere; current divides across paths. Two equal resistors in parallel halve the resistance — more paths, easier flow, like adding lanes to a highway.

The voltage divider

Two resistors in series split the voltage proportionally — the cheapest "make a smaller voltage" trick there is:

Vout = Vin × R2 / (R1 + R2)

Worked example: 5V in, two 10kΩ resistors:

Vout = 5 × 10000 / (10000 + 10000) = 2.5 V

Check (verified): 2.5 V. (Caveat: dividers are for signals, not power — anything you connect draws current and shifts the ratio. For powering things, use a regulator — see Power Supplies.)

Battery life estimation

hours = battery_mAh / draw_mA

Worked example: 2000 mAh battery, circuit draws 20 mA:

2000 / 20 = 100 hours

Check (verified): ~100 hours, in ideal conditions. Real life is less (batteries fade, draw varies) — treat it as an upper bound, not a promise.

Next: Components