Ohm's Law

A phone charger's label might say "5 V 2 A". The first number is the voltage it gives. The second is the most current it can supply. One equation links them with a third quantity, resistance. You will use it in almost every lesson after this one.

Current, voltage and resistance

A circuit is a closed path that current flows around: out of a battery, through the parts and back to the battery.

Electric charge is what electrons carry. Current is charge on the move: how much charge flows past a point each second. It is measured in amperes (A), or amps. One amp is one coulomb per second, and a coulomb is a fixed amount of charge, about 6.24 × 10¹⁸ electrons.

Current flowing through a part is what makes it do something. It warms a wire, spins a motor and lights an LED (light-emitting diode): a small part that lights up when current flows through it, like the power light on many chargers.

Voltage is how hard the supply pushes charge from one point to another. It is measured in volts (V), and its formal name is potential difference. The supply is whatever provides the voltage, such as a battery or a USB port. An AA cell (a single battery unit) gives 1.5 V, a USB port gives 5 V, and a car's electrical system runs at about 12 V.

Voltage is always measured between two points. One point on its own has no voltage. So you pick one point in the circuit and call it 0 V. That point is ground (GND), and it is usually the battery's negative end. When a lesson says "the output is 3 V", it means 3 V measured from ground. A schematic, a circuit drawing with symbols for parts and lines for wires, marks ground with its own symbol.

Resistance is how much something opposes current. It is measured in ohms (Ω). A long, thin wire has more resistance than a short, thick one. That is why the jumper cables used to start a car are so thick. A resistor is a part made to have a set resistance: the small striped part with two wire legs that you find in any beginner's kit.

Voltage is measured across a part, between its two ends. Current flows through it.

The law

For a resistor, the three quantities are linked:

V = I × R

Rearranged as you need it: I = V / R and R = V / I. One ohm is the resistance that lets 1 V drive 1 A.

Try it below. Under Solve for, pick the quantity you want the instrument to work out, then set the other two. It starts at 9 V and 470 Ω, which gives 19.1 mA. The "m" stands for milli-, one thousandth, so 19.1 mA (milliamps) is 0.0191 A.

The law says three things:

• More voltage across the same resistor gives more current. A harder push moves more charge.
• More resistance with the same voltage gives less current.
• A current through a resistor makes a voltage across it. Beginners often miss this one, but you will use it a lot. Most USB power meters (the small boxes that sit between a charger and a phone cable) read current this way: they measure the voltage across a tiny resistor in the current's path, called a shunt.

Power: where the energy goes

When current flows through a resistance, the resistance turns electrical energy into heat. This is called dissipating the energy. How fast energy turns into heat is power, measured in watts (W):

P = V × I

Put Ohm's law into it and you get the two forms you will use most:

P = I² × R and P = V² / R

The charger from the opening can give at most 5 V × 2 A = 10 W. A charging cable that feels warm is turning a little of that into heat in the resistance of its wires.

Power goes with the square of the current. Double the current through a resistor and it makes four times the heat. So a part that runs warm at 1 A can burn out at 2 A.

Every part has a power rating: the most power it can turn into heat without damage. The resistors with wire legs in a beginner's kit are usually 1/4 W. The tiny surface-mount resistors soldered flat onto a board, like most of the parts in a phone, are often 1/10 W. The instrument's Power readout adds a note when the heat passes 1/10 W and again past 1/4 W.

The water-pipe picture, and its limits

A common picture: voltage is water pressure, current is how much water flows, and resistance is a narrow section of pipe. The picture works for everything in this module.

It gets two things wrong:

• Charge is not used up. Water leaves a tap and is gone. Electrons are not consumed: as many return to the battery as leave it. What gets used up is energy, not charge. When a TV remote's batteries go flat, they have run out of energy, not electrons. This is also why a circuit must be a closed path. If you cannot trace the path back to where it started, no current flows.
• Electrons are slow, but the push is fast. Each electron drifts through copper at well under a millimetre per second. Yet a flashlight lights the moment you press its button, because the push travels along the wire at a large fraction of the speed of light. In this module the difference does not matter. It matters again in module 11, on circuit boards.

Worked example

A USB port's 5 V lights a red LED through a 220 Ω resistor in line with it. The resistor sets how much current the LED gets. A red LED typically takes about 2.0 V of the 5 V. This is its voltage drop: the voltage across a part while current flows through it. The resistor gets the rest:

• Voltage across the resistor: 5 V − 2.0 V = 3.0 V
• Current: I = 3.0 V / 220 Ω = 13.6 mA
• Power in the resistor: P = 3.0 V × 13.6 mA = 40.9 mW

A milliwatt (mW) is a thousandth of a watt. To check the numbers, set the instrument to 3 V and 220 Ω. 40.9 mW is well under a 1/4 W (250 mW) rating.

Now use the same 220 Ω resistor with a 24 V supply. The resistor gets 24 V − 2.0 V = 22 V, so the current is 22 V / 220 Ω = 100 mA, and the resistor turns 2.2 W into heat. That is almost nine times its 1/4 W rating, so it overheats and fails.