# Power Consumed in a Resistor

Current flowing through a resistor causes power to be dissipated as *heat* or *thermal energy*. For this reason, the *maximum power rating* of the resistor must not be exceeded or the resistor may overheat – probably causing its destruction.

The maximum power which may be safely dissipated by a resistor will depend on a number of factors such as its physical size, construction type, ambient temperature, maximum operating temperature, plus any external cooling arrangements such as heatsinks or fans. Carbon film, metal film or metal foil resistors may be used in low power applications with typical ratings of 0.125 W, 0.25 W. 0.5 W, 1 W or 2 W. Wirewound resistors are typically used for larger power applications (up to 1,000 W or even more), and these are normally fitted to a suitable heatsink to prevent overheating.

The most commonly used form of the resistor power equation states that the power (P - watts) is given by the product of the voltage (V - volts), multiplied by the current (I - amperes).

#### Worked Example 1

**a)** Calculate the power consumed in a 1 kΩ resistor if the voltage is 10 V and the current is measured as 10 mA (0.01 A). Hence select a suitable power rating for the resistor.

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*P* = *V* × *I*

= 10 × 0.01

= 0.1 W

A 0.25 W resistor would be suitable.

**b)** If the maximum voltage is increased to 100 V, calculate the new minimum power rating.

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Before starting, it's important to realise that the current will have risen to 0.1 A, according to Ohm's law (*I* = *V* ÷ *R* = 100 / 1,000 = 0.1 A).

*P* = *V* × *I*

= 100 × 0.1

= 10 W

Notice that increasing the voltage by a factor of 10 increases the power consumed by 100 times! This is caused by both the voltage and current increasing by a factor of ten.

## Alternative Forms

Two alternative forms of the resistor power equation are available, and these may prove useful if either *V* or *I* is unknown.

Different forms of the resistor power equation may be found by substituting Ohm's law into the basic expression, in order to eliminate the unwanted variable. See the resistor power problems page for more details.

The second form may be used where the voltage is unknown:

#### Worked Example 2

Calculate the power consumed in a 27 Ω resistor if the current is 0.1 A. Hence suggest a suitable power rating for the resistor.

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*P* = *I*^{2} × *R*

= 0.1 × 0.1 × 27

= 0.27 W

A 0.5 W resistor would be suitable.

The third and final variation of the resistor power equation is useful where the current is unknown.

#### Worked Example 3

Calculate the power consumed in a 330 Ω resistor if the applied voltage is 12 V.

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*P* = *V*^{2} / *R*

= 12 × 12 × / 330

= 0.44 W to 2 d.p.

A 0.5 W resistor would be suitable.