Ohm's Law

One-sentence summary

Ohm's Law is a simple rule that describes how voltage, current and resistance affect each other in a circuit, written as V = I × R.

Why does it matter?

If you connect an LED straight to a battery, it may shine brightly for a second, then dim or even burn out. The reason is that too much current flows through it. This is exactly where Ohm's Law helps: it lets you work out how much resistance to add before anything gets damaged.

Once you learn this law, you stop guessing. Instead of saying "I hope it survives," you calculate the right resistor. When you build a robot, choose a motor driver, connect a sensor or safely light an LED, you keep using the same three quantities: voltage, current and resistance.

Three basic quantities

To understand Ohm's Law, let us first meet three words. Thinking about them as a water pipe makes them much easier.

Voltage (V)

Voltage is the force that pushes electricity through a circuit. Its unit is the volt (V). In the water-pipe picture, voltage is like the pressure that pushes the water. The higher the pressure, the harder the water flows.

Example: Two AA batteries in series give about 3 volts, while a USB cable provides 5 volts.

Current (I)

Current is the amount of electric charge flowing through a circuit. Its unit is the ampere (A). In the water pipe, current is like the amount of water passing through the pipe. More pressure lets more water flow.

In small circuits the current is usually tiny, so we use milliamperes (mA). 1000 mA = 1 A. A typical LED runs comfortably at 20 mA, which is 0.02 amperes.

Resistance (R)

Resistance is what makes it harder for current to flow. Its unit is the ohm (Ω). In the water pipe, resistance is like how narrow the pipe is. The narrower the pipe, the less water passes through.

Example: When you add a resistor to a circuit, it limits the current, meaning it reduces the electricity flowing through. That is why we place a small resistor next to an LED.

Short definition: Ohm's Law says voltage pushes current and resistance limits it. The formula is V = I × R.

How the formula connects everything

The formula V = I × R can be written three ways. All three are the same rule seen from a different side:

Voltage    = Current × Resistance    V = I × R
Current    = Voltage ÷ Resistance    I = V ÷ R
Resistance = Voltage ÷ Current       R = V ÷ I

You can picture the formula as a triangle:

      V
    -----
   I  |  R

V sits on top, with I and R below. Cover the quantity you are looking for with a finger and read what is left:

• Cover V and you are left with I × R.
• Cover I and you are left with V ÷ R.
• Cover R and you are left with V ÷ I.

How they affect each other

• If resistance stays the same and you raise the voltage, the current rises too.
• If voltage stays the same and you raise the resistance, the current drops.
• That is why, when we want less current, we add a bigger resistor.

With the water picture: raise the pressure (voltage) and more water (current) flows; make the pipe narrower (resistance) and less water flows.

Simple worked examples

Now let us use real numbers. It matters that you work in amperes: divide milliamperes by 1000 to get amperes.

Example 1: Finding the current

A circuit has 6 volts and a 300 ohm resistor. What is the current?

I = V ÷ R
I = 6 ÷ 300
I = 0.02 amperes = 20 mA

A current of 20 milliamperes flows through the circuit.

Example 2: Finding the resistance

You apply 3 volts and want 0.01 amperes (10 mA) to flow. What resistor do you need?

R = V ÷ I
R = 3 ÷ 0.01
R = 300 ohms

You would use a 300 ohm resistor.

Practice: A current-limiting resistor for an LED

This is the calculation you will do most often in electronics. To light an LED safely, we place a correctly sized resistor next to it. This resistor is called a current-limiting resistor.

An LED always drops a small voltage across itself. For a red LED this is usually about 2 volts. Let our source be a 5 volt USB, and let us aim for a safe LED current of 20 mA (0.02 A).

First we find the voltage across the resistor. The source gives 5 V, the LED takes 2 V, so the voltage left for the resistor is:

Voltage across resistor = Source - LED
                        = 5 V - 2 V
                        = 3 V

Now we use Ohm's Law to find the resistance:

R = V ÷ I
R = 3 ÷ 0.02
R = 150 ohms

So a 150 ohm resistor lets about 20 mA flow through the LED. If you cannot find exactly 150 ohms, choosing the next slightly larger value (such as 180 ohms) is safe. A slightly bigger resistor means slightly less current; the LED still lights, but with more safety margin.

The text schematic of the circuit looks like this:

[+ 5V USB] --- [150 Ω resistor] --- [LED ►|] --- [- GND]
   (+)                              anode  cathode  (-)

The direction of the LED matters: the long leg (anode) faces the plus side and the short leg (cathode) faces the minus side. If you connect it backwards, the LED will not light.

Mini practice

A small calculation you can do with pencil and paper. You can ask an adult to check it.

You have two AA batteries (about 3 volts) and a green LED. The green LED drops about 2 volts, and you want 10 mA (0.01 A) to flow through it.

1. Find the voltage left across the resistor (source minus LED).
2. Use Ohm's Law to calculate the resistor you need.
3. Draw the text schematic of the circuit.

Write down your answer before checking, then compare it with the solution in the "Answers" section.

Common mistakes

Forgetting to convert milliamperes to amperes

In the formula you must use current in amperes. If you write 20 mA directly, your answer is off by 1000 times. Divide by 1000 first: 20 mA = 0.02 A.

Connecting an LED without a resistor

Without a resistor, too much current flows through the LED and it can be damaged. There should always be a current-limiting resistor beside an LED.

Using the full source voltage

When calculating the resistor, use the voltage across the resistor, not the whole source. First subtract the voltage the LED takes (for example 2 V).

Connecting the LED backwards

If the long leg does not go to plus and the short leg to minus, the LED will not light. Check the direction before connecting.

Safety note

• Use only low-voltage educational sources: batteries (2×AA, 3–6 V), USB, micro:bit or Arduino. Never experiment with mains electricity, wall sockets or exposed wiring.
• Have an adult nearby when you work with batteries, motors, cutting tools and hot surfaces.
• When building the circuit, connect the polarity correctly, avoid short circuits, and always use a resistor beside an LED.
• Be careful with lithium batteries: a short circuit or wrong connection can cause heat and danger. Disconnect a battery that gets hot right away and tell an adult.

Lesson summary

• Ohm's Law links three quantities: voltage (V), current (I) and resistance (R).
• The basic formula is V = I × R, also written as I = V ÷ R and R = V ÷ I.
• Voltage pushes current and resistance limits it; think of water pressure and a narrow pipe.
• When calculating, use current in amperes (divide mA by 1000).
• For an LED, the current-limiting resistor is (source − LED voltage) ÷ current. A 5 V source and a 2 V LED at 20 mA needs 150 ohms.

Check questions

1. What is the basic formula of Ohm's Law?
2. In the water-pipe picture, what does resistance look like?
3. In a circuit with 12 volts and a 600 ohm resistor, what is the current in amperes?
4. Why do we place a current-limiting resistor next to an LED?
5. If the source is 5 V, the LED drops 2 V and we want 20 mA, what resistor do we need?

Answers

1. V = I × R (voltage equals current times resistance).
2. It is like how narrow the pipe is; the narrower the pipe, the less current flows.
3. I = V ÷ R = 12 ÷ 600 = 0.02 amperes, which is 20 mA.
4. The resistor limits the current through the LED. Without it, very high current would damage the LED.
5. First the voltage across the resistor: 5 − 2 = 3 V. Then R = 3 ÷ 0.02 = 150 ohms.

Mini practice solution: Voltage across the resistor is 3 − 2 = 1 V. The resistor needed is R = 1 ÷ 0.01 = 100 ohms. Schematic: [+ 3V battery] --- [100 Ω] --- [LED ►|] --- [- GND].

Source and verification note

For “Ohm's Law”, verification focuses on whether the relationship between Three basic quantities and Current (I) remains consistent across examples. Activities are designed only for low-voltage direct-current circuits; mains electricity is not used. Component values must be rechecked for the actual circuit, and connections should be reviewed with an adult before power is applied.

Next lesson

How Does a Breadboard Work? We will learn the hole layout and the hidden connections of the breadboard that let you build circuits without soldering.