Ohm’s Law

For many materials, the current that flows is directly proportional to the voltage [latex]V[/latex] applied across the material. The German physicist Georg Simon Ohm (1787–1854) demonstrated experimentally that, for a metal wire under many everyday conditions, the current is proportional to the applied voltage:

This relationship is known as Ohm’s law. It is best thought of as an empirical (experiment-based) rule: voltage is the “cause” and current is the “effect.” Like friction laws, it describes what is often observed in real materials, but it is not guaranteed to hold in every situation. Many devices and materials—such as diodes, many biological tissues, and superconductors—do not show a simple proportionality between [latex]I[/latex] and [latex]V[/latex].

Resistance and Simple Circuits

If voltage drives current, what impedes it? The electric property that opposes current (loosely analogous to friction) is called resistance [latex]R[/latex]. Collisions of moving charges with atoms, ions, and molecules transfer energy to the material and limit how easily charges can drift through it. In many situations, current decreases as resistance increases:

For example, if resistance doubles (with the same applied voltage), the current is cut in half. Combining the proportionalities
[latex]I\propto V[/latex] and [latex]I\propto 1/R[/latex] gives the most common equation form of Ohm’s law:

In this form, Ohm’s law essentially defines resistance for materials that behave linearly. Materials for which [latex]I[/latex] is proportional to [latex]V[/latex] are called ohmic. For an ohmic material, the resistance [latex]R[/latex] is constant—it does not change when you change [latex]V[/latex] or [latex]I[/latex] (within the operating range and temperature conditions).

An object designed to provide a specific resistance is called a resistor, even if its resistance is small. The unit of resistance is the ohm, with symbol [latex]\Omega[/latex] (Greek capital omega). Rearranging [latex]I=V/R[/latex] gives [latex]R=V/I[/latex], so:

Figure 20.1 shows a schematic for a simple circuit. A simple circuit has a single voltage source and a single resistor. The connecting wires are often treated as having negligible resistance (or their resistance is included in [latex]R[/latex]).

Resistances span many orders of magnitude. Some ceramic insulators (such as those supporting power lines) can have resistances of
[latex]10^{12}~\Omega[/latex] or more. A dry person may have a hand-to-foot resistance around
[latex]10^{5}~\Omega[/latex], while the resistance of the human heart is about
[latex]10^{3}~\Omega[/latex]. A meter-long piece of thick copper wire may have resistance near
[latex]10^{-5}~\Omega[/latex], and superconductors have essentially no resistance at all (they are non-ohmic).
Resistance depends on both the material and the shape of the object, as we will see in a later section on resistance and resistivity.

Additional insight comes from solving [latex]I=\frac{V}{R}[/latex] for voltage:

This expression describes the voltage drop (often called the [latex]IR[/latex] drop) across a resistor when a current [latex]I[/latex] flows through it. In a circuit, the voltage increases across the source and decreases across resistive elements. This is closely analogous to fluid flow:
a voltage source is like a pump that creates a pressure difference, and a resistor is like a narrow pipe that reduces pressure and limits flow.

Conservation of energy is central here. The voltage source supplies energy to charges (creating an electric field and causing current), and the resistor converts that energy into other forms (often thermal energy, sometimes light). In a simple circuit with one resistor, the voltage supplied by the source equals the voltage drop across the resistor because the same charge [latex]q[/latex] flows through the entire loop and the energy per charge is [latex]\Delta V[/latex]. (See Figure 20.2.)