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Resistor

2 June, 2016 - 15:17
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Figure 3.2 Resistor. v = Ri  
 

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)

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 \frac{1}{R}. 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.

p(t)=Ri^2(t)=\frac{1}{R}v^2(t)

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.