Use Ohm's law, resistor color codes, voltage dividers, RC circuits and LED resistors to size parts for a simple circuit, and know the limits of the formulas. Flags the 4 mistakes that most often produce a plausible-but-wrong answer.
Key takeaways
- Ohm's law: voltage equals current times resistance, and power equals voltage times current.
- Series resistances add, and parallel resistances combine to less than the smallest.
- A voltage divider needs a load much larger than its lower resistor.
- An LED needs a series resistor sized from the supply, its forward voltage and the current you want.
- The RC time constant is resistance times capacitance, and about 63 percent of the change happens in one constant.
Voltage, current and resistance
Voltage is the push, current is the flow and resistance is the opposition. Ohm's law ties them together: voltage equals current times resistance. A 100 ohm resistor with 2 amps through it drops 200 volts. Power is voltage times current, so the same numbers dissipate 400 watts, which is why real parts have power ratings and get hot.
Reading resistor color bands
A four-band resistor carries two digits, a multiplier and a tolerance. Brown, black and red mean 1, 0 and times 100, which is 1,000 ohms, and a gold band adds a 5 percent tolerance. Read from the end away from the tolerance band. The real value can sit anywhere within the tolerance, so measure with a meter when precision matters.
Resistors in series
In series, current has one path and the resistances add. Two resistors of 100 and 220 ohms make 320 ohms in a chain. The voltage across the chain splits in proportion to the resistances. Series connection is the way to build a larger value from smaller ones, and it always raises the total.
Resistors in parallel
In parallel, current has several paths and the total falls. The reciprocal of the total is the sum of the reciprocals, so 100, 220 and 330 ohms together come to about 57 ohms, less than the smallest. Adding a path can only lower the resistance. Two equal resistors in parallel give exactly half of one.
The voltage divider
Two resistors in series divide a voltage in proportion to their values, and the output is taken across the lower one. With 12 volts across 10,000 and 5,000 ohms, the output is 4 volts. Anything connected to the output draws current, which pulls the voltage down, so keep the load much larger than the lower resistor. A divider suits signals and sensors, and not power.
Sizing an LED resistor
An LED's current rises steeply with voltage once it turns on, so a resistor sets the current. Subtract the LED's forward voltage from the supply and divide by the current you want. On 12 volts with a 2 volt LED at 20 milliamps, the result is 500 ohms. Round up to the next standard value, 560 ohms, which runs the LED a little below its full current and keeps it safe.
Standard resistor values
Resistors come in preferred values, such as the E12 series, which has twelve steps per decade: 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68 and 82. A calculated value rarely matches one exactly, so choose the next value up when you are protecting a part and the nearest when precision is the goal.
RC circuits and time
A resistor and a capacitor together set how quickly a voltage changes. The time constant is resistance times capacitance: 10,000 ohms and 100 microfarads give 1 second. After one time constant a charging capacitor reaches about 63 percent of its final value, and after 4.6 constants about 99 percent. The same product sets the cutoff frequency of a simple filter.
From watts to amps
Appliances list power in watts, and wiring is sized by current. Divide the watts by the voltage and the power factor to get amps. An 1,800 watt heater on 120 volts draws 15 amps. Motors have a power factor below one, so they draw more current than their wattage suggests, and three-phase supplies share the load across lines.
Safety and limits
These formulas describe ideal parts. Real components have tolerances, temperature effects and power limits, and mains voltage is dangerous. Work on low-voltage circuits while you learn, check ratings before you build, and leave mains wiring to a qualified electrician. A calculator confirms the arithmetic and does not replace judgment.
Worked with real numbers
What this looks like in the ohm's law calculator
The guidance above is easier to judge against figures. Using the ohm's law calculator worked example, moving current (amps) from 1.6 to 2.4 changes the voltage from 160 to 240.
| Current (amps) | Voltage | Power (watts) |
|---|---|---|
| 1.6 | 160 | 256 |
| 1.8 | 180 | 324 |
| 2 | 200 | 400 |
| 2.2 | 220 | 484 |
| 2.4 | 240 | 576 |
Open the Ohm's Law Calculator to use your own numbers →
The inputs behind those figures
| Input | Value | Definition |
|---|---|---|
| Current (amps) | 2 | Enter the current (amps) used in this calculation. |
| Resistance (ohms) | 100 | Enter the resistance (ohms) used in this calculation. |
What goes wrong
Common mistakes
Each of these produces an answer that looks reasonable, which is why they survive review. To catch them in electronics basics: ohm's law, resistors, dividers and leds, rerun the ohm's law calculator with a different assumption and check whether the result moves in the direction the guidance predicts, since an error that survives that test is usually in one of the inputs and not in the arithmetic.
| The mistake | Why it misleads | Do this instead |
|---|---|---|
| Reading the color bands from the wrong end | The tolerance band belongs on the right, and reading backward gives a different value. | Put the gold or silver band on the right before you read. |
| Adding resistances in parallel | The parallel total is always smaller than the smallest part, and a plain sum is far too large. | Use the reciprocal rule, or the parallel result in the resistor calculator. |
| Rounding an LED resistor down | A smaller resistor passes more current than planned and shortens the LED's life. | Round up to the next standard value. |
| Using a divider to power a load | It wastes energy in the resistors and the output sags as the load draws current. | Use a regulator for power and a divider only for signals. |
People also ask
Frequently asked questions
What is Ohm's law?
Voltage equals current times resistance. It links the three quantities for a resistive part.
How do I read a resistor's color code?
Take the first two bands as digits, the third as the multiplier and the fourth as the tolerance. The resistor color code calculator does it.
How do I calculate resistors in parallel?
Add the reciprocals of each resistance and take the reciprocal of the sum. The result is smaller than the smallest resistor.
What resistor do I need for an LED?
Subtract the LED's forward voltage from the supply voltage and divide by the current. The LED resistor calculator also gives the next standard value.
What is an RC time constant?
The product of resistance and capacitance, the time for a capacitor to charge to about 63 percent of the way.
How do I convert watts to amps?
Divide watts by volts times the power factor. For three-phase, divide by the square root of three as well.
What is a voltage divider used for?
To reduce a voltage to a fraction of the input for a signal or a sensor. It is a poor way to supply power.
Why does my LED resistor get hot?
The resistor drops the difference between the supply and the LED's forward voltage at the LED's current, and that power appears as heat. Check the power rating, which the LED resistor calculator shows.
What is the E12 series?
A set of twelve preferred resistor values per decade, from 10 to 82. Most resistors are made in these values, so a calculated value is rounded to a standard one.
Can I put resistors in series to get a value I do not have?
Yes. Series resistances add, so two resistors give a larger value. In parallel the total is lower than the smallest.
Which input moves the voltage most in the ohm's law calculator?
Ranked by how far each moves the voltage across the range tested: current (amps) (40, 20%) and resistance (ohms) (40, 20%).
If I double current (amps) in the ohm's law calculator, does the voltage double?
Doubling it from 2 to 4 takes the voltage from 200 to 400, which is 2.00 times the worked-example figure. So the result scales almost exactly in proportion. Halving it to 1 gives 100.