Learn › Topic 1

Ohm's Law and Electric Power: A Guide with Examples

7 min read · bitGateLab Team

Almost every calculation in electronics starts with three quantities: voltage, current and resistance. Ohm's law ties them together in a single formula, and power tells you how much energy is turned into heat every second. Here you'll learn to use both, to read a resistor's value from its color bands and to pick one that won't burn out. With that, you can already work out the resistor for an LED, check whether a circuit is properly sized and make sense of what a multimeter shows.

Voltage, current and resistance

The voltage (V, in volts) is the potential difference between two points: it is what "pushes" the charges. Current (I, in amperes) is the amount of charge that passes a point each second. Resistance (R, in ohms, Ω) measures how strongly an element opposes the flow of that current.

In a linear resistor, the current is proportional to the applied voltage. That is Ohm's law:

V = I · R        I = V / R        R = V / I

If you double the voltage across a fixed resistance, the current doubles. If you double the resistance at the same voltage, the current drops by half. It pays to work with prefixes: a voltage in volts divided by a resistance in kΩ gives the current directly in mA (12 V / 4 kΩ = 3 mA).

Basic circuit: the current leaves through the positive terminal (the long plate), flows through the resistor and returns to the negative terminal.

Example 1. A 12 V source drives a 470 Ω resistor, as in the figure. How much current flows?

I = V / R = 12 V / 470 Ω.
I = 0.02553 A ≈ 25.5 mA.

Electric power

Electric power (P, in watts) is the rate at which an element receives or delivers energy. For any element, P = V · I. In a resistor, all of that power is turned into heat. Substituting Ohm's law gives two more forms, very handy when you only know two of the quantities:

P = V · I        P = I² · R        P = V² / R

Notice the square: if you double the current in a resistor, the heat it produces is multiplied by four. That is why wires carrying a lot of current get so hot even though their resistance is small.

The energy consumed is power times time: E = P · t. A 60 W device left on for 3 hours uses 180 Wh, that is, 0.18 kWh.

Example 2. In the previous circuit (12 V, 470 Ω), how much power does the resistor dissipate?

Using P = V² / R: P = 144 / 470 = 0.306 W.
Check with P = V · I: 12 V × 0.02553 A = 0.306 W. It matches.
A common 1/4 W (0.25 W) resistor would overheat. You need at least a 1/2 W one, and preferably 1 W to leave some headroom.

Resistor color code

Through-hole resistors carry colored bands that indicate their value. In the four-band code, the first two bands are digits, the third is the multiplier (a power of 10) and the fourth is the tolerance. The tolerance band is usually set slightly apart from the others; start reading from the opposite end.

Color	Digit	Multiplier	Tolerance
Black	0	×1	—
Brown	1	×10	±1 %
Red	2	×100	±2 %
Orange	3	×1 000	—
Yellow	4	×10 000	—
Green	5	×100 000	±0.5 %
Blue	6	×1 000 000	±0.25 %
Violet	7	—	±0.1 %
Gray	8	—	±0.05 %
White	9	—	—
Gold	—	×0.1	±5 %
Silver	—	×0.01	±10 %

Examples: brown-black-red-gold is 10 × 100 = 1 000 Ω = 1 kΩ ±5 %. Yellow-violet-orange-gold is 47 × 1 000 = 47 kΩ ±5 %. Red-red-brown is 22 × 10 = 220 Ω. In the five-band code (precision resistors) there are three digits before the multiplier.

The tolerance tells you the range in which the actual value may lie. A 1 kΩ ±5 % resistor can measure anywhere between 950 Ω and 1 050 Ω and still be within spec.

Power rating: choosing the right resistor

Besides its value in ohms, every resistor has a power rating: the most power it can dissipate continuously without being damaged. The most common through-hole ratings are 1/8 W, 1/4 W, 1/2 W, 1 W and 2 W; the larger the body, the more heat it can handle. The rule of thumb is to choose a power rating of at least twice the power you calculated, because the resistor is also heated by its surroundings and by nearby components.

Example 3. You want to light a red LED from 5 V. The LED drops about 2 V and you want about 15 mA to flow through it.

The voltage the resistor has to take up is 5 V − 2 V = 3 V.
R = 3 V / 0.015 A = 200 Ω. The next standard value up is 220 Ω.
With 220 Ω: I = 3 V / 220 Ω = 13.6 mA, enough for the LED to shine brightly.
Power in the resistor: P = 3 V × 0.0136 A = 0.041 W = 41 mW.
A 1/4 W (250 mW) resistor is more than enough; even a 1/8 W (125 mW) one satisfies the factor-of-two rule.

Key point: Ohm's law describes linear resistors. An LED, a diode or an incandescent bulb does not obey V = I · R with a fixed value of R; that is why, in the LED example, we applied Ohm's law only to the resistor.

Common mistakes

Mixing units: dividing volts by kΩ and writing the result in amperes. Volts divided by kΩ give mA.
Calculating the power with the source voltage instead of the voltage that actually drops across the resistor.
Choosing a resistor by its value in ohms alone and forgetting the power rating.
Reading the color code backwards, starting from the gold or silver band.
Assuming that a small increase in current barely changes the heat: power grows with the square of the current.

Try it in the simulator

Checking Ohm's law with measurements is the best way to make it stick. In the simulator you can build the circuit in the figure and measure everything with no risk of burning anything out.

Place a DC voltage source and set it to 12 V.
Place a 470 Ω resistor and connect it across the source terminals.
Connect the multimeter in series to measure the current and compare it with the 25.5 mA you calculated.
Measure the voltage across the resistor with the multimeter in parallel.
Change the source voltage to 6 V and then to 24 V; notice that the current changes in the same proportion.
Calculate the power in each case and see how it quadruples when the voltage doubles.

Exercises

A 1.8 kΩ resistor is connected to 9 V. Calculate the current and the power.

Show answer

I = 9 V / 1.8 kΩ = 5 mA. P = 9 V × 5 mA = 45 mW.
A resistor has the bands orange-orange-red-gold. What is its value, and between what values can it measure?

Show answer

33 × 100 = 3 300 Ω = 3.3 kΩ ±5 %. It can measure between 3 135 Ω and 3 465 Ω.
You have a 100 Ω, 1/4 W resistor. What is the maximum voltage you can apply to it, and how much current would flow in that case?

Show answer

From P = V² / R: V = √(0.25 × 100) = √25 = 5 V. The current would be I = 5 V / 100 Ω = 50 mA. Check: 5 V × 0.05 A = 0.25 W. To leave some headroom, it is best to stay well below that limit.
A heater runs on 24 V and draws 1 A. What are its resistance and its power, and how much energy does it use in 2 hours?

Show answer

R = 24 V / 1 A = 24 Ω. P = 24 V × 1 A = 24 W. E = 24 W × 2 h = 48 Wh (0.048 kWh).

Next step: learn to analyze circuits with several branches in Kirchhoff's Laws.