Ohm's first law

When a current $i$ flows through a resistor, a potential difference appears across its terminals. Ohm’s first law states that, for a broad class of materials (ohmic conductors), this potential difference is directly proportional to the current: doubling the current doubles the voltage drop.

Key formula — Ohm's first law

The potential difference across a resistor carrying current $i$ is $\ev{\Delta V = R\,i}$ where $R$ is the component’s resistance.

The proportionality constant $R$ is the resistance, which measures how much the component obstructs the passage of current: for a given applied voltage, a large resistance lets little current through. It is measured in ohms (symbol $\Omega$), a unit defined as volts over amperes:

$\ev{[\,R\,] = \Omega = \frac{\mathrm{V}}{\mathrm{A}}}$

A resistor has a resistance of one ohm if, carrying a current of one ampere, it shows a potential difference of one volt across its terminals.

Potential drops in the direction of the current

Crossing the resistor in the direction of the current, the potential decreases: the current flows “downhill”, from the point at higher potential to the one at lower potential, giving up energy as it goes. This is why $\Delta V = Ri$ is also called the voltage drop.

Returning to the hydraulic analogy, the potential drop across the resistor is like the pressure difference at the two ends of a narrow pipe: the narrower the pipe (large resistance), the greater the pressure drop needed to push the same flow rate of water (current) through it.

Dissipated power

The energy that charges lose crossing the resistor does not vanish: it turns into heat. The dissipated power can be written in three equivalent forms

$P = R\,i^2 = \Delta V\cdot i = \frac{(\Delta V)^2}{R}$

all obtained by combining Ohm’s first law with the definition of electrical power. This phenomenon, the Joule effect, is explored in more depth in a dedicated atom.

Try it — circuit simulator

Connect a resistor to a source and verify Ohm’s first law: current is proportional to voltage, with resistance as the constant of proportionality.

CircuitJS simulator by Paul Falstad (GPLv2).

Links

Topics: Circuiti elettrici Concepts: Legge di Ohm

Related exercises: Problem — resistance of a light bulb · Problem — resistance and power of an ohmic conductor · Problem — voltage drop in a copper cable