Electronics Basics for Students: Resistor Colour Codes, Ohm's Law and Number Systems Explained

Whether you build with an Arduino, an ESP32 or just a breadboard, three basics come up again and again: reading resistors, Ohm's law and number systems. This guide explains each with worked examples, and shows where the free resistor calculator and number converter can check your answers.

Part 1: The resistor colour code

A resistor limits the flow of current. Its value is printed as coloured bands. In a 4-band resistor, the first two bands are digits, the third is a multiplier and the fourth is the tolerance. A 5-band resistor has three digit bands, then the multiplier and the tolerance.

Examples

• Yellow, violet, red, gold: 4, 7, ×100, ±5% gives 4,700 Ω, which is 4.7 kΩ ±5%.
• Brown, black, orange, gold: 1, 0, ×1,000, ±5% gives 10 kΩ ±5%.
• Green, blue, black, brown, brown (5-band): 5, 6, 0, ×10, ±1% gives 5,600 Ω, which is 5.6 kΩ ±1%.

Hold the resistor with the gold or silver band on the right, and read from the left. If you are unsure, measure it with a multimeter, or enter the colours in the resistor calculator.

Part 2: Ohm's law

Ohm's law links voltage (V), current (I) and resistance (R):

V = I × R, so I = V ÷ R and R = V ÷ I.

Power is P = V × I, which tells you how much heat a part must handle. A common small resistor is rated for about a quarter of a watt.

Example: which resistor for an LED?

You power a red LED from the 5 V pin of an Arduino. The LED needs about 2 V and you want about 20 mA (0.02 A).

1. Voltage left for the resistor: 5 V − 2 V = 3 V.
2. Resistance: R = 3 ÷ 0.02 = 150 Ω.
3. Choose a standard value at or above this, such as 150 Ω or 220 Ω. With 220 Ω the current is 3 ÷ 220 ≈ 14 mA, which is safe and bright enough.

On a 3.3 V board such as the ESP32, the same LED leaves 1.3 V for the resistor. For about 10 mA, R = 1.3 ÷ 0.01 = 130 Ω, so a 150 Ω resistor works and gives about 8.7 mA.

Resistors in series and parallel

• Series: add the values. 1 kΩ + 2 kΩ = 3 kΩ.
• Parallel: the total is less than the smallest one. Two 1 kΩ resistors in parallel give 500 Ω. For two resistors, use (R1 × R2) ÷ (R1 + R2).

Part 3: The voltage divider

Two resistors in series divide a voltage:

Vout = Vin × R2 ÷ (R1 + R2), where Vout is measured across R2.

Example: to bring a 5 V signal down for a 3.3 V board, use R1 = 1 kΩ and R2 = 2 kΩ. Vout = 5 × 2,000 ÷ 3,000 ≈ 3.33 V. This is how many students connect the 5 V echo pin of an HC-SR04 to an ESP32 pin. Use it for signals only, and not to power parts that draw current. A divider is also how an LDR or thermistor becomes a voltage a board can read.

Part 4: Binary, octal, decimal and hexadecimal

The same number can be written in different bases. Computers use binary (base 2), people use decimal (base 10), and programmers often use hexadecimal (base 16) because it is a short way to write binary.

Binary to decimal

Add the powers of two for each digit that is 1. For 1010, the digits from the right are worth 1, 2, 4 and 8, so 8 + 2 = 10.

Binary to hexadecimal

Split the binary number into groups of four bits from the right, and convert each group. 1111 0000 becomes F and 0, so the result is F0, which is 240 in decimal. This is why I2C addresses, memory addresses and colour codes such as #FF0000 are written in hex.

Check any conversion in the number converter, which handles large numbers exactly.

Put it to use

• Use Ohm's law to pick the LED resistor, and check the value with the resistor calculator.
• Use a divider to protect a 3.3 V pin from a 5 V sensor, as explained in our Arduino versus ESP32 guide.
• Try the 12 beginner Arduino projects, which use these ideas from the first circuit.
• Generate starter sketches with the Arduino code generator.

Gopafy's IoT Lab offers project kits with circuit diagrams and documentation for engineering students. Whatever you build, check your calculations and learn why each value was chosen, because that is what examiners ask.