# Circuit Theory/Resistors

## Resistors

Mechanical engineers seem to model everything with a spring. Electrical
engineers compare everything to a **Resistor**. Resistors are circuit
elements that resist the flow of current. When this is done a voltage
appears across the resistor\'s two wires.

A pure resistor turns electrical energy into
heat. Devices similar to resistors turn this energy into light, motion,
heat, and other forms of energy.

![](Resistor_schema.png "Resistor_schema.png")

Current in the drawing above is shown entering the + side of the
resistor. Resistors don\'t care which leg is connected to positive or
negative. The + means where the positive or red probe of the volt meter
is to be placed in order to get a positive reading. This is called the
\"positive charge\" flow
sign convention. Some circuit theory classes (often within a physics
oriented curriculum) are taught with an \"electron flow\" sign
convention.

In this case, current entering the + side of the resistor means that the
resistor is removing energy from the circuit. This is good. The goal of
most circuits is to send energy out into the world in the form of
motion, light, sound, etc.

## Resistance

**Resistance** is
measured in terms of units called \"Ohms\" (volts per ampere), which is
commonly abbreviated with the Greek letter Ω (\"Omega\"). Ohms are also
used to measure the quantities of *impedance* and *reactance*, as
described in a later chapter. The variable most commonly used to
represent resistance is \"r\" or \"R\".

Resistance is defined as:

$$r = {\rho L \over A}$$

where ρ is the resistivity of the material, L is the length of the
resistor, and A is the cross-sectional area of the resistor.

## Conductance

**Conductance** is the inverse of resistance. Conductance has units of
\"Siemens\" (S), sometimes referred to as mhos (ohms backwards,
abbreviated as an upside-down Ω). The associated variable is \"G\":

$$G = \frac{1}{r}$$

Before calculators and computers, conductance helped
reduce the number of hand calculations that
had to be done. Now conductance and it\'s related concepts of
admittance and susceptance can be
skipped with matlab, octave, wolfram alpha and other computing tools.
Learning one or more these computing tools is now absolutely necessary
in order to get through this text.

## Resistor terminal relation

right\|framed\|A simple circuit diagram relating current, voltage, and
resistance

The drawing on the right is of a battery and a resistor. Current is
leaving the + terminal of the battery. This means this battery is
turning chemical potential energy into electromagnetic potential energy
and dumping this energy into the circuit. The flow of this energy or
power is negative.

Current is entering the positive side of the resistor even though a +
has not been put on the resistor. This means electromagnetic potential
energy is being converted into heat, motion, light, or sound depending
upon the nature of the resistor. Power flowing out of the circuit is
given a positive sign.

The relationship of the voltage across the resistor V, the current
through the resistor I and the value of the resistor R is related by
ohm\'s law:

$$V=R*I$$

A resistor, capacitor and inductor all have only two wires attached to
them. Sometimes it is hard to tell them apart. In the real world, all
three have a bit of resistance, capacitance and inductance in them. In
this unknown context, they are called two terminal devices. In more
complicated devices, the wires are grouped into
ports. A two terminal device
that expresses Ohm\'s law when current and voltage are applied to it, is
called a resistor.

## Resistor Safety

Resistors come in all forms. Most have a maximum power rating in watts.
If you put too much through them, they can melt, catch fire, etc.
Resistance is an electrical passive element which oppose the flow of
electricity. Air can be considered as one of the resistances. Air is
used as a resistance in Lightning Arrestors. Also vacuum also is used as
a resistor.

## Example

Suppose the voltage across a resistor\'s two terminals is 10 volts and
the measured current through it is 2 amps. What is the resistance?

If $v=iR$ then $R = v/i = 10V/2A = 5 ohms$
