the SI unit of electrical resistance, named after Georg Simon Ohm. An ohm is equivalent to a volt per ampere. Since resistors are specified and manufactured over a very large range of values, the derived units of milliohm (1 mΩ = 10−3 Ω), kilohm (1 kΩ = 103 Ω), and megohm (1 MΩ = 106 Ω) are also in common usage. Series and parallel resistors The total resistance of resistors connected in series is the sum of their individual resistance values. The total resistance of resistors connected in parallel is the reciprocal of the sum of the reciprocals of the individual resistors. For example, a 10 ohm resistor connected in parallel with a 5 ohm resistor and a 15 ohm resistor produces ohms of resistance, or = 2.727 ohms. A resistor network that is a combination of parallel and series connections can be broken up into smaller parts that are either one or the other. Some complex networks of resistors cannot be resolved in this manner, requiring more sophisticated circuit analysis. Generally, the Y-Δ transform, or matrix methods can be used to solve such problems. Power dissipation At any instant, the power P (watts) consumed by a resistor of resistance R (ohms) is calculated as: where V (volts) is the voltage across the resistor and I (amps) is the current flowing through it. Using Ohm's law, the two other forms can be derived. This power is converted into heat which must be dissipated by the resistor's package before its temperature rises excessively. Resistors are rated according to their maximum power dissipation. Discrete resistors in solid-state electronic systems are typically rated as , , or watt. They usually absorb much less than a watt of electrical power and require little attention to their power rating. Power resistors are required to dissipate substantial amounts of power and are typically used in power supplies, power conversion circuits, and power amplifiers; this designation is loosely applied to resistors with power ratings of 1 watt or greater. Power resistors are physically larger and may not use the preferred values, color codes, and external packages described below. If the average power dissipated by a resistor is more than its power rating, damage to the resistor may occur, permanently altering its resistance; this is distinct from the reversible change in resistance due to its temperature coefficient when it warms. Excessive power dissipation may raise the temperature of