# Power Dissipation Calculator

Created by Davide Borchia
Last updated: Jul 10, 2022

Our power dissipation calculator will be helpful both with your homework, your experiments, and even if you just wonder why electronic devices get hot.

• What is power dissipation in an electronic circuit;
• How to calculate the power dissipated by a resistor: the two dissipated power equations;
• How to calculate the dissipated power in parallel and series circuits; and
• Why is power dissipation a curse and a blessing at the same time?

## What is power dissipation?

Dissipation is an unavoidable side effect of using electronic components, for which a certain amount of heat is released into the environment during the device's operations.

In the field of electromagnetism, the dissipated power is the result of the flow of a current in a resistive material (for example, a wire's resistance).

The dissipated power is measured in watts (or multiples and submultiples). You can use non-SI units, but they are way less common than this one. Visit our power converter to learn how to convert between them.

The dissipated power originates from the loss of energy due to the development of the voltage drop across a resistance (thanks to Ohm's law), causing a loss of potential energy. While in other physical systems, the energy can dissipate in other forms, heat is the only means in electromagnetism.

## How do I calculate the power dissipation?

To calculate the power dissipated by a resistor, you need to know two of the following quantities:

• The resistance $R$;
• The electric current $I$; or
• The voltage drop $V$.

There are two possible formulas for power dissipation. The first one requires you to know resistance and current:

$P = R\cdot I^2$

Alternatively, if you know the current and the voltage drop, you can use the other formula for power dissipation:

$P= V\cdot I$

The two equations are totally equivalent, and at a quick glance, you can see the action of Ohm's law: $V=R\cdot I$.

## How to calculate the power dissipated by resistors in series and parallel

You can calculate the power dissipation of a single resistor or of systems of them. We identify two main types of resistors placement in a circuit:

Technically, you can apply the dissipated power equation on each of the resistors, taking care to use the correct values of current/voltage drop for each component (you can calculate them with Kirchoff's law). However, this process is unnecessarily cumbersome. A system of resistors (if resistors only are used in the circuit) can be reduced to a single equivalent resistor. Once the value of this "imaginary" component is known, we can apply the equation for the dissipated power just once.

#### Power dissipated in a set of series resistors

To calculate the equivalent resistance in a series circuit, we can simply multiply the current flowing in the circuit by the sum of the values of resistance:

\begin{align*} P& = I^2\cdot (R_1+R_2+...+R_n)\\ P&=I^2\cdot R_{\text{EQ}} \end{align*}

Since the current flowing in the resistors is not varying from one component to the other, we can factor it out in the dissipated power formula.

If you know the voltage drop, apply Ohm's law, and find the value of $I$ this way.

#### Power dissipated in a set of parallel resistors

If the resistors are in a parallel circuit, the current branches in each of them: we can't simply sum the values of the resistance.

To calculate the equivalent resistance, we apply the following formula:

\begin{align*} \frac{1}{R_{\text{EQ}}}&=\frac{1}{R_1}+\frac{1}{R_2}+...+\frac{1}{R_n} \end{align*}

Once you know this value, apply Ohm's law to find the current flowing in the circuit and calculate the dissipated power with the formula:

$P=I^2\cdot R_{\text{EQ}}$

## Why is power dissipation a problem?

Power dissipation is the reason your devices get hot when you are using them. Every component has a resistance, as you know, and when in use, they contribute to the heat emitted by your phone or computer. The CPU, in particular, is densely packed with transistors, is a great source of heat, and is also a critical component to cool down.

This is why, if you open your computer to sneak a peek, you'll see the CPU directly connected to a heat sink and covered by a layer of thermal paste: all of these precautions contribute to keeping the temperature of your computer's brain at acceptable levels.

On the other hand, power dissipation is the reason electric heaters work: by using a highly resistive material, they dissipate great amounts of power.

Davide Borchia
Voltage
V
Connection type
Series
Resistor 1 (R₁)
Ω
Resistor 2 (R₂)
Ω
You can add up to 10 resistors, fields will appear as you need them.
Results
Input at least one resistor to obtain a result.
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