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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.
![v(t)=Ri(t)](/system/files/resource/9/9648/9696/media/eqn-img_1.gif)
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.
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