What is a resistor?

An ideal resistor is a two-terminal device in which the voltage across the terminals is proportional to the current flowing through the device. The constant of proportionality is denoted as $R$, the resistance of the device. This resistance is measured in units of volts per ampere or ohms (denoted by the Greek symbol $\Omega$). In mathematical terms, this relationship is written as

$$v(t) = R i(t)$$ (1)

where $R$ is the resistance, $v(t)$ is the voltage across the resistor, and $i(t)$ is the current flowing through the resistor. Equation 1 is usually called Ohm's Law.

The symbol for a resistor is shown by the lefthand picture in figure 2. The righthand picture in figure 2 depicts the actual component. From this picture you will find that the resistor is a small cylindrical component with two wire leads coming out of each end. Often the device will have colored bands around it. These bands are a color code specifying the value of the resistor in $ohms$.

Figure 2: Resistor

Equation 1 is the equation for a linear resistor. The linearity of the device can be readily appreciated if we draw the current-voltage characteristic or I-V curve for the device. This curve plots the voltage $v(t)$ across the device as a function of the current $i(t)$ through the device. Figure 3 shows the I-V characteristic for a linear resistor. This characteristic is a straight line. The resistance is given by the slope of the line.

Figure 3: A linear resistor and its I-V characteristic

Two special types of resistors are the short circuit and open circuit. We define a short circuit as a two-terminal device device whose resistance is zero. An open circuit is a two-terminal device whose resistance is infinite.

A special type of a resistor is a potentiometer. We sometimes refer to them as pots. The potentiometer has three terminals. There are two terminals at either end of a resistor ($a$ and $c$) and a third terminal connection (called the wiper) that taps into the middle of the resistor. The lefthand picture in figure 4 shows the symbol for a potentiometer, which is a resistor with the wiper lead tapping into the middle of the device. The righthand picture shows the physical device. This particular trim pot has a dial on the front that allows you to mechanically adjust the position of the wiper. The first and third leads on the bottom of the device correspond to the two ends of the resistor and the wiper lead is the lead in the middle.

You can use the potentiometer to construct a resistor whose resistance changes when you change the wiper position (by turning the dial on the front of the pot). This is simply done by connecting lead $a$ to the circuit and connecting the wiper (lead $b$) to the circuit. The lefthand picture in figure 4 shows which two leads you must connect in order to get a variable resistor. By changing the dial position you can change the resistance between leads $a$ and $b$.

Figure 4: A variable resistor