The resistor is far and away the simplest circuit element. In a resistor, the voltage is proportional to the current, with the constant of proportionality R, known as the resistance.
Resistance has units of ohms, denoted by Ω, named for the German electrical scientist Georg Ohm5 . Sometimes, the v-i relation for the resistor is written i = Gv, with G, the conductance, equal to . Conductance has units of Siemens (S), and is named for the German electronics industrialist Werner von Siemens .
When resistance is positive, as it is in most cases, a resistor consumes power. A resistor's instantaneous power consumption can be written one of two ways.
As the resistance approaches infinity, we have what is known as an open circuit: No current flows but a non-zero voltage can appear across the open circuit. As the resistance becomes zero, the voltage goes to zero for a non-zero current flow. This situation corresponds to a short circuit. A superconductor physically realizes a short circuit.