Ohm's Law

Ohm's Law

Ohm's Law states that the voltage of an electric current (i.e., the potential difference between the two ends of the examined element) is linearly proportional to the current flowing through that element, with resistance as the proportionality constant.

\begin{aligned} U = R \cdot I \end{aligned}

In another formulation, Ohm's Law states that the ratio of voltage to current is constant and depends solely on resistance, not on other factors.

Ohm's Law is valid only for a certain group of materials and under specific conditions. It applies only to linear conductors (most metals, some ceramic materials) at a constant temperature. However, it is preserved for both alternating and direct current.

Resistance / Conductor Resistance

As mentioned, the proportionality constant that determines how difficult it is to increase the current is resistance (resistivity). The unit of resistance is Ohm:

\begin{aligned} [R]= 1 \, \Omega = 1 \, \text{V/A} \end{aligned}

Sometimes the concept of conductance is used – the inverse of electrical resistance:

\begin{aligned} \sigma = \frac{1}{\rho} \end{aligned}

Resistance is proportional to the length of the conductor l and inversely proportional to its cross-section S, with the proportionality constant being the specific resistance ρ:

\begin{aligned} R = \rho \cdot \frac{l}{S} \end{aligned}

Where:

• ρ – specific resistance [Ω·m]
• l – length of the conductor [m]
• S – cross-sectional area [m²]

Sometimes electrical conductivity is used – the inverse of resistance:

The table below lists the specific resistances of selected materials.

Current Characteristics as a Function of Voltage

To better understand both what we mean by linear dependence and how it differs from nonlinear, let's take a look at the graphs of linear and nonlinear resistors.