Resistors

The damper of the electrical domain is the resistor. What makes something a resistor is that it establishes a relationship between voltage and current -- not, for instance, between voltage and charge, which we will see is what a capacitor does.

Simple off-the-shelf components of the electrical domain are much more linear, in practice, than those of the mechanical or hydraulic domains. The constitutive law of a $0.05 resistor is so straight there is no point in graphing it. It relates voltage V to current i via a propotionality constant called the resistance R, measured in ohms. The greek letter omega W indicates ohms. KW is kilo-ohms (103 W), and MW is mega-ohms (106 W ). This is called Ohm's law
V = R i
(1)
The symbol for a resistor in a circuit diagram is the jagged line. It's usually annotated with the resistance (in ohms). Often a current or voltage is labeled as well.

means:

By now we are all very tired of explicitly drawing meters in order to make clear what is meant by a positive value of the associated dynamic variable. Although you will often want to make an indication of the + and - ends of your voltmeter, especially when you write Kirchoff's loop law, we will use the following consistent convention:

When the direction of positive current is indicated as it is by the arrow in figure 1, that will be used to imply both the polarity of the voltage measurement across the resistor (or other component, except for batteries), as well as that of the current measurement through the resistor, as shown in figure 2. For batteries, since they are labelled with a + and - end, we will always take our voltmeter across them to be consistent with their markings. Choosing meter polarities is further explained here.
Real voltmeters and ammeters have a red + probe and a black - probe, just as shown. When current is flowing into the + end and out the - end of an ammeter, the meter reports a positive result. When the voltage across the resistor, and therefore also across the voltmeter, is such that the potential is higher at the red + probe than at the black - probe, the voltmeter reports a positive result.

Equation (1) is for voltage and current defined as in the figure above. Because it relates voltage to current with a plus sign, it says that the voltage and current in a resistor are always of the same sign. This is true, for resistors. Current wants to flow downhill, from higher potentials to lower, just as hydraulic flows will tend to go from higher pressure to lower. A resistor lets current pass, in a quantity and direction proprtional to its desire (voltage).

Other electrical components will not necessarily have a positive current through them when there is a positive voltage across them, even though the meaning of positive dynamic variables (i and v) will be just as in the figures above.


Power

Like mechanical dampers, resistors can only absorb power. They cannot store it, so they can never be the source of a flow of power to another component. Power flowing into a resistor is dissipated as heat. With the standard sign definitions for current and voltage, the power flowing into any component, not just a resistor, is P = iV. For resitors, i and V always have the same sign, per the constitutive law (1), so power flowing into a resistor can never be negative. For components which can have i and V of different signs, power may be either positive or negative.
P = i V
(2)
Power is measured in watts. A watt is an amp*volt. A watt*second is a joule, the same unit of energy we used in the mechanical domain. Evidently the kilowatt*hour for which Commonwealth Edison charges you $0.10 is a lot of energy: 3.6 million joules, or about enough to put a 1 kg mass into orbit.

 


Recognizing a resistor

The above are actual resistors used in circuits. Sometimes they are labeled with text stating their resistance and power rating. However, more often than not, the colored lines are used to identify them. For more pictures of resistors, and information on how to identify the color codes, click here.

The next obvious question, is "what is a resistor made of"?? Click here to see inside a few resistors.