Ohm's Law: Voltage, Current and Resistance

What Ohm's law says

In a circuit made of resistance, the current equals the voltage divided by the resistance. Rearranged, that becomes the formula most electricians learn first: V = I × R.

• Voltage (V) is the electrical pressure that pushes current around a circuit. It is measured in volts.
• Current (I) is the rate at which charge flows past a point. It is measured in amperes, usually shortened to amps.
• Resistance (R) is how strongly a material opposes that flow. It is measured in ohms, written with the symbol Ω.

Raise the voltage across a fixed resistance and the current rises with it, in direct proportion. Raise the resistance at a fixed voltage and the current falls. Every calculation in this lesson comes back to those two facts.

The letter I comes from intensité, the French term for current intensity used by André-Marie Ampère. It is easy to confuse with the number 1, so write it clearly on a job sheet.

Try it on a working circuit

The circuit below has a voltage source, a resistor, an ammeter in line with the current and a voltmeter across the resistor. Choose which value to solve for, then move the other two. Tap any part of the drawing to see what it does.

The moving dashes show how much current is flowing: more current, faster dashes. They follow conventional current, which runs from the positive terminal through the load and back to the negative terminal. The electrons themselves drift the opposite way, and far more slowly than the animation suggests.

Solving for any one value

Because V = I × R is a simple product, you can rearrange it to find whichever value is missing.

A quick memory aid is the Ohm's law triangle: V on top, with I and R side by side underneath. Cover the value you want to find. What remains shows the math, either a division (V over I, or V over R) or a multiplication (I beside R).

Power: what the circuit does with the energy

For a resistive load, voltage and current together tell you how much power it uses, measured in watts. A resistor turns that power into heat, which is what a heater element is built to do.

Substituting Ohm's law gives two more forms of the same formula: P = I² × R and P = V² ÷ R. Use whichever one matches the numbers you have.

That is most of a 15 A circuit for one appliance. Plug a 1500 W hair dryer into the same circuit and the total climbs to 25 A, well past the breaker rating, so the breaker trips.

Why loose connections run hot

Ohm's law explains one of the most common causes of electrical fires. A loose, corroded or undertightened connection adds resistance at a point where there should be almost none, and every amp of load current has to pass through it.

Forty watts spread across a light bulb is ordinary. Forty watts concentrated in a single screw terminal can discolor insulation, loosen the connection further and eventually start a fire. Because the heat rises with the square of the current, the same bad connection produces four times the heat when the current doubles.

Measuring the voltage drop across a connection under load is a standard way to find these problems: a sound connection drops almost nothing, while a reading across a single terminal points to added resistance. That measurement is made on energized equipment, so it is work for qualified people using rated meters and the right protective equipment.

Where the simple model stops

Ohm's law describes resistive loads well. A few things change the picture in real installations.

• Temperature. Resistance changes as materials heat up. A cold incandescent filament has a small fraction of its hot resistance, so the bulb draws a surge of current the instant it turns on.
• Alternating current with reactance. Motors, transformers and capacitors add reactance, and the combined opposition to current is called impedance (Z). The same idea holds, written V = I × Z. For these loads, volts times amps gives volt-amperes (VA). Multiply by the power factor, a number below 1, to get the real power in watts.
• Electronic loads. LED drivers, chargers and variable speed drives do not draw current in proportion to the voltage, so no single resistance value describes them.

For purely resistive loads on alternating current, such as heaters and incandescent lamps, Ohm's law works with the RMS values a meter reads. That is why the 120 V examples in this lesson hold up.

Check your understanding

Where this knowledge gets used

• Journeyman openings: Journeymen use these numbers every day, from checking a load to tracking down heat at a bad connection.
• Starting out in the trade: How registered apprenticeships work, what they ask of you and how long they take.
• Pay by market: See what electrical work pays in the markets near you.

Related lessons

• Series and Parallel Circuits: Wire the same three lamps two ways, then burn one out, short one and overload the breaker. See why buildings are wired in parallel.
• How Three-Way Switches Work: Flip two switches and watch one light. Follow the travelers, switch between a schematic and a hallway view, and track down a wiring mistake.