Ohm's Law Explained: V = IR With Worked Examples

Ohm's law says that the current through a conductor is proportional to the voltage across it, as long as its temperature stays the same. Written as a formula, V = IR: voltage (V, in volts) equals current (I, in amps) times resistance (R, in ohms, Ω). Double the voltage across a 10 Ω resistor and the current doubles too.

What do voltage, current and resistance mean?

These three quantities describe every circuit, so it helps to have a clear picture of each before using the formula.

• Current (I) is the rate at which charge flows past a point. It is measured in amps (A) with an ammeter, connected in series. 1 A means 1 coulomb of charge passing every second.
• Voltage (V), or potential difference, is the energy each coulomb of charge transfers between two points. It is measured in volts (V) with a voltmeter, connected in parallel across the component. 1 V means 1 joule per coulomb.
• Resistance (R) is how hard it is for current to flow through a component. It is measured in ohms (Ω). A component has a resistance of 1 Ω if a voltage of 1 V drives a current of 1 A through it.

A common picture: voltage is the push, current is the flow, and resistance is how narrow the pipe is. A bigger push gives more flow; a narrower pipe gives less.

What is the Ohm's law formula?

The ohm's law formula is V = IR, and it rearranges into three forms depending on what you want to find:

You want	Formula	In words
Voltage	V = I × R	current times resistance
Current	I = V ÷ R	voltage divided by resistance
Resistance	R = V ÷ I	voltage divided by current

The formula triangle is an easy way to remember it: write V at the top, I and R side by side underneath. Cover the one you want, and the other two show you what to do. Cover V and you see I R side by side (multiply). Cover R and you see V over I (divide).

The law is named after Georg Ohm, a German physicist who published it in 1827 after measuring currents through wires of different lengths and thicknesses.

How to calculate resistance, current and voltage

The method is the same every time: write down what you know with units, convert to amps, volts and ohms, pick the right form of the formula, then put the units on your answer.

Example 1: finding current

A 12 V battery is connected across a 4 Ω resistor. What current flows?

I = V ÷ R = 12 ÷ 4 = 3 A

Example 2: finding voltage

A current of 0.5 A flows through a 20 Ω resistor. What is the voltage across it?

V = I × R = 0.5 × 20 = 10 V

Example 3: how to calculate resistance

A bulb has 9 V across it and an ammeter in series reads 300 mA. What is the bulb's resistance?

First convert: 300 mA = 0.3 A. Then R = V ÷ I = 9 ÷ 0.3 = 30 Ω

That last step catches people out more than any other. Always change mA into A and kΩ into Ω before you divide.

What is an ohmic conductor?

An ohmic conductor is a component that obeys Ohm's law: its resistance stays the same whatever the current. A metal wire or a fixed resistor at constant temperature is ohmic. Plot current (I) against voltage (V) and you get a straight line through the origin, and the line is the same if you reverse the voltage.

Plenty of components don't behave like this:

• Filament lamp. As the current rises the filament heats up, its metal ions vibrate more and get in the way of the electrons, so resistance goes up. The I–V graph curves over and gets flatter at high voltage.
• Diode. Current flows easily one way and hardly at all the other way. The graph is flat along the axis for negative voltages, then shoots up once the forward voltage passes about 0.6 V for a silicon diode.
• Thermistor. Its resistance falls as it gets hotter, which is why thermistors are used in thermostats.
• LDR (light-dependent resistor). Its resistance falls in bright light.

V = IR still tells you the resistance of any of these at one particular moment. What changes is that R is no longer a constant, so the component isn't ohmic.

How does Ohm's law work in series and parallel circuits?

Ohm's law applies to every component and to the circuit as a whole, once you know the total resistance.

• In series the resistances add: R = R₁ + R₂ + …. A 6 V supply across 2 Ω and 4 Ω in series sees 6 Ω in total, so I = 6 ÷ 6 = 1 A. The same 1 A flows through both, so the 2 Ω resistor has 2 V across it and the 4 Ω one has 4 V. The voltages add up to the supply.
• In parallel each branch gets the full supply voltage, and the currents add. The total resistance is less than the smallest branch: 1/R = 1/R₁ + 1/R₂. Two 10 Ω resistors in parallel give 5 Ω.

How is Ohm's law related to power?

Electrical power is P = IV, in watts. Combine it with V = IR and you get two more useful forms: P = I²R and P = V² ÷ R. A 30 Ω bulb with 0.3 A through it uses P = 0.3² × 30 = 2.7 W. These forms explain why power lines use high voltage: for the same power, a smaller current means far less energy wasted heating the cables (the I²R loss).

Common mistakes with Ohm's law

• Forgetting to convert units. 250 mA is 0.25 A; 2.2 kΩ is 2200 Ω.
• Using the wrong voltage. In a series circuit, use the voltage across that component, not the supply voltage, when you work out its resistance.
• Putting meters in the wrong way. Ammeter in series, voltmeter in parallel. A voltmeter in series stops the current almost completely.
• Saying a lamp "obeys Ohm's law". It doesn't: its resistance rises as it heats up.
• Leaving off units, or writing "Ω" for a current. Units are often worth a mark on their own.

For a page of every electricity equation in one place, see Physics formulas. To see a curved graph of a different kind, read the best angle for maximum range.

Frequently asked questions

Is Ohm's law always true?

No. Ohm's law only holds for ohmic conductors, such as metal wires and fixed resistors, and only while their temperature stays the same. A filament lamp, a diode or a thermistor doesn't obey it, because its resistance changes with the current or the conditions. It describes how certain materials behave, not a universal law like conservation of energy.

What is the unit of resistance?

Resistance is measured in ohms, written with the Greek letter omega (Ω). One ohm is the resistance that lets a current of one amp flow when one volt is across it, so 1 Ω = 1 V/A. Larger resistances are given in kilohms (1 kΩ = 1000 Ω) and megohms (1 MΩ = 1,000,000 Ω).

Does a higher resistance mean less current?

Yes, as long as the voltage stays the same. Current equals voltage divided by resistance, so doubling the resistance halves the current and tripling it cuts the current to a third. That's how a resistor protects an LED: it limits the current so the LED doesn't overheat and burn out.

What is the difference between voltage and current?

Current is how much charge flows past a point each second, measured in amps. Voltage is how much energy each unit of charge gives up between two points, measured in volts. Voltage is the cause and current is the effect: no voltage across a component means no current through it, however low its resistance.

Try it yourself

Open the Circuit Builder and wire a cell, a resistor and an ammeter in a loop, then put a voltmeter across the resistor. Note the readings, then change the cell's voltage a few times. Divide each voltmeter reading by the ammeter reading: for a resistor you get the same answer every time. Swap the resistor for a bulb and try it again.