A hydraulic analogy is sometimes used to describe Ohm`s law. Water pressure, measured by Pascal (or PSI), is the analogue of voltage, because the creation of a difference in water pressure between two points along a (horizontal) pipe causes water to flow. The flow of water, as in liters per second, is the analogue of current, as in coulombs per second. After all, flow limiters – such as openings in pipes between points where water pressure is measured – are the analogue of resistors. We say that the flow of water through an orifice limiter is proportional to the difference in water pressure through the reflector. Similarly, the flow rate of the electric charge, i.e. the electric current, through the electrical resistance is proportional to the voltage difference measured through the resistance. where e {displaystyle e} , m e {displaystyle m_{e}} and v e {displaystyle mathbf {v} _{e}} are the charge, mass and velocity of the electrons. In addition, ν {displaystyle nu } is the frequency of collisions of electrons with ions that have a velocity field v i {displaystyle mathbf {v} _{i}}. Since the electron has a very small mass compared to the ions, we can ignore the left side of the equation above to write that Ohm`s law is applicable when physical conditions such as temperature are kept constant. where l is the length of the conductor in units SI of meters, a is the area of cross-section (for a round wire a = πr2 if r is of radius) in units of square meters and ρ is the resistivity in units of ohmmeters. where V and I are the complex scalar in voltage and current respectively and Z are the complex impedance.

where I is the current passing through the conductor in units of amps, V is the voltage measured through the conductor in units of volts, and R is the resistance of the conductor in units of ohms. Specifically, Ohm`s law states that the R is constant in this regard, regardless of current. [3] If the resistance is not constant, the previous equation cannot be called Ohm`s law, but it can still be used as the definition of static/DC resistance. [4] Ohm`s law is an empirical relationship that accurately describes the conductivity of the vast majority of electrically conductive materials in many current orders. However, some materials do not obey Ohm`s law; These are called non-ohmic. where ρ = σ − 1 {displaystyle rho =sigma ^{-1}} is the electrical resistance. It is also common to write η {displaystyle eta } instead of ρ {displaystyle rho }, which can be confusing because it is the same notation used for magnetic diffusivity, which is defined as η=1/μ 0 σ {displaystyle eta =1/mu _{0}sigma }. In this approach, a voltage or current waveform takes the form Aest, where t is time, s is a complex parameter, and A is a complex scalar.

In any time-invariant linear system, all currents and voltages can be expressed with the same parameter s as the input of the system, so that the complex exponential term varying in time can be cancelled and the system can be described algebraically with respect to complex scalars in current and voltage waveforms. where we used the definition of current density and also defined σ = n e e 2 ν m e {displaystyle sigma ={n_{e}e^{2} over nu m_{e}}} which is the electrical conductivity. This equation can also be written equivalently as where J is the current density at a given location in a resistive material, E is the electric field at that location, and σ (sigma) is a material-dependent parameter called conductivity. This reformulation of Ohm`s law goes back to Gustav Kirchhoff. [5] Ohm`s law, description of the relationship between current, voltage and resistance. The amount of constant current through a large number of materials is directly proportional to the difference in potential or voltage between materials. Thus, if the voltage V (in units of volts) between two ends of a wire made of one of these materials is tripled, the current I (amperes) also triples; and the quotient V/I remains constant. The quotient V/I for a given piece of material is called resistance R, measured in units called ohms.

The strength of materials to which Ohm`s law applies does not change over huge voltage and current ranges. Ohm`s law can be expressed mathematically as V/I = R. The fact that the resistance or voltage/current ratio is generally constant for all or part of an electrical circuit at a fixed temperature was established in 1827 by the research of the German physicist Georg Simon Ohm.