When designing precision electronics or performing a detailed worst-case analysis, one quickly learns to consider parameters that may not be so important in other applications. One of the more interesting things to learn is that the tolerance of a resistor is just the starting point. It does not actually define the maximum or minimum value the resistor could be within your circuit.
The key parameters associated with a resistor are as follows.
Tolerance: This defines how close to the nominal value is allowable for the resistor when it is manufactured. A nominal 1,000Ω resistor with a tolerance of ±5% will have a value ranging between 950 and 1,050Ω. This value will be fixed; the value of the resistor will not vary during its life due to the tolerance. However, the engineer has to consider the tolerance in design calculations and ensure the circuit will function across the entire potential value range.
Temperature coefficient: This describes how the value of the resistor changes as a function of temperature. It is defined as parts per million/Kelvin; common values are 5, 10, 20, and 100 PPM/K. Actually, the best way to think of this is parts per million per ohm/Kelvin. A 1,000Ω resistor with a temperature coefficient of 100 PPM experiencing a ±60K temperature change over the operating temperature range (240-360K, based on an ambient room temperature of 300K) will experience a resistance change of ±6Ω based on its nominal value. Obviously, the lower the temperature coefficient, the more expensive the resistor will be. (This is the same for low-tolerance resistors.)
Resistor self-heating: For really high-precision circuits, it is sometimes necessary to consider the power dissipation within the resistor. The resistor will have a specified thermal resistance from the case to ambient, and this will be specified in °C/W. The engineer will know the power dissipation within the resistor; this can be used to determine the temperature rise and hence the effect on the resistance.
To determine the maximum and minimum resistance applicable to your resistor, you must consider the tolerance, the temperature coefficient, and the self-heating effect. As you perform your analysis, you may notice some of the parameters are negligible and can be discounted, but you have to consider them first to know whether or not you can discount them.
For some precision circuits (gain stages in amplifiers, for example) it may be necessary to match resistors to ensure their values are within a specified tolerance of each other and have the same temperature coefficients.
In certain circuits, it is also important to make sure that critical resistors are positioned correctly to ensure both terminal ends of the resistor are subjected to the same heating or cooling effects. Otherwise, the Seebeck effect may need to be considered. When using forced airflow, for example, it may be necessary to ensure that both resistor terminals are perpendicular to the airflow, so the component is of uniform temperature.