# Power Dissipation Calculator

Created by Purnima Singh, PhD
Reviewed by Steven Wooding
Last updated: Sep 27, 2022

Use Omni's power dissipation calculator to determine the power dissipated in series and parallel resistor circuits. Just enter the applied voltage and the resistances of the resistors. The calculator will calculate the equivalent resistance of the circuit, the total current through the circuit, and the power dissipated by the resistors.

If you are only interested in calculating the equivalent resistance of a circuit, you can check out our series resistor calculator and parallel resistor calculator.

Continue reading to know what power dissipation is and the formula to calculate the power dissipated by resistors. You will also find an example of how to find the power dissipated in a circuit.

## What is power dissipation?

According to Ohm's law, when an electric current passes through a resistor, a voltage drop occurs across its end. This means that some electric potential energy is lost when the electric charge moves from one end of the resistor to the other. This potential energy is converted to heat, and we call this conversion (or loss) dissipation. Thus, power dissipation is the loss of electric potential energy (per unit time) in the form of heat by an electrical device when a current flows through it.

Although power dissipation is an undesirable effect, there are instances where this phenomenon is of great use, for example, in electric heaters.

## Power dissipation formula

To calculate the power $P$ dissipated by a resistor $R$ when a current $I$ passes through it, we will use Joule's law of heating:

$\quad \scriptsize P = I^2R$

We can also substitute Ohm's law into the above equation to get:

$\quad \scriptsize P = VI \\ \text {...or:} \\ \quad P = \frac{V^2}{R}$

You can use any of the three formulas mentioned above to calculate the power dissipated by resistors.

The power dissipated by a resistor appears in the form of heat, i.e., the resistor gets heated when current flows through it. The maximum power that a resistor can dissipate without burning is called the power rating of a resistor.

## Power dissipation in a series circuit

In a series circuit (see figure 1), the circuit's total resistance (or equivalent resistance) is the sum of the individual resistances.

$\quad \scriptsize R_{eq} = R_1 + R_2 + ... + R_n$

If we connect a voltage source $V$, to this circuit, the same current $I$ will flow sequentially through all the resistors. We can calculate the total current in a series circuit using Ohm's law:

$\quad \scriptsize I = \frac{V}{R_{eq}}$

The power dissipated by each resistor is:

$\quad \scriptsize P_1 = I^2R_1, P_2=I^2R_2, ....., P_n = I^2R_n$

The total power dissipated by the circuit is:

$\quad \scriptsize P = P_1 +P_2 + .... + P_n \\ \quad P = I^2 R_{eq}$

...and the total power supplied by the voltage source (e.g., a battery) is:

$\quad \scriptsize P = I V$

## Power dissipation in a parallel circuit

Let us consider a circuit consisting of parallel combination of resistors, $R_1$, $R_2$, ...., $R_n$ (see figure 2). We can determine the total resistance in a parallel circuit using the formula:

$\quad \scriptsize \frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + .... + \frac{1}{R_n}$

If we connect a voltage source $V$ across this combination, the total current in the parallel circuit is:

$\quad \scriptsize I = \frac{V}{R_{eq}}$

In a parallel combination of resistors, the voltage drop across each resistor is the same. Hence we can calculate the power dissipation across each resistor as:

$\quad \scriptsize P_1 = \frac{V^2}{R_1}, P_2=\frac{V^2}{R_2}, ....., P_n = \frac{V^2}{R_n}$

The total power dissipated by the circuit is:

$\quad \scriptsize P = P_1 +P_2 + .... + P_n \\ \quad P = \frac{V^2}{ R_{eq}}$

## How to calculate power dissipation?

Let us see how to calculate power dissipation in a series circuit using the power dissipation calculator. We will consider a circuit consisting of three resistors connected in series across a battery with a voltage output of 12.0 V. Let the three resistors be $R_1= 2\ \Omega$, $R_2= 6\ \Omega$, and $R_3= 1\ \Omega$.

1. Enter the voltage output of the battery, e.g., 12.0 V.
2. Choose the connection type series, using the drop-down menu.
3. Enter the resistance of the three resistors, e.g., $R_1= 2\ \Omega$, $R_2= 6\ \Omega$, and $R_3= 1\ \Omega$.
4. You can add up to 10 resistors, as new rows will appear as you type the resistances.
5. The result section of the calculator will display the equivalent resistance of the circuit (9 Ω) and the total current through the circuit (1.3 A).
6. The calculator will also determine the power dissipated by the individual resistors (3.6 watt, 11 watt, and 1.8 watt, respectively) and the total power dissipated (16 watts).

You can also use this calculator just to calculate the total current in a parallel circuit or a series circuit.

Do you know that we call power consumed by resistors the active power and power consumed by inductors or capacitors the reactive power? Read more about active and reactive power on our three phase calculator.

## FAQ

### How do I find power dissipated in a series circuit?

To find the power dissipated in a series circuit, follow the given instructions:

1. Add all the individual resistances to get the total resistance of the series circuit.
2. Divide the voltage by the total resistance to get the total current in a series circuit.
3. In a series circuit, the same current flows through each resistor.
4. Multiply the square of the current with the individual resistances to get the power dissipated by each resistor.
5. Add the power dissipated by each resistor to get the total power dissipated in a series circuit.

### How do I find power dissipated in a parallel circuit?

To find the power dissipated in a parallel circuit, follow these steps:

1. Find out the voltage supplied by the source.
2. In a parallel connection, the voltage drop is the same across each resistor.
3. Divide the square of the voltage by the individual resistors to get the power dissipated by each resistor.
4. Add the power dissipated by individual resistors to get the total power dissipated by the parallel circuit.

### Is more power dissipated in series or parallel circuit?

A parallel circuit dissipates more power than a series circuit. For the same set of resistors, the total resistance of the parallel circuit is always lower than the total resistance in a series circuit.

Since the power dissipated in a circuit is inversely proportional to the resistance of the circuit for a constant voltage source, a parallel connection will dissipate more power than a series circuit.

### Which resistor dissipates more power in series (or parallel) connection?

In a series circuit, the highest value resistor dissipates the most power. This is because the same current sequentially flows through each resistor in a series connection, and the power dissipated is directly proportional to the resistance.

In a parallel connection, the power dissipated is inversely proportional to the resistance, as the voltage drop is the same across each resistor. Hence, the lowest value resistor dissipates the most power.

### How to calculate heat dissipation from power consumption?

To determine the heat dissipation from power consumption, multiply the power consumed (in watts) by the time (in seconds) for which the current flows.

### How do I calculate power rating?

To calculate the power rating of any electrical appliance, use the given steps:

1. Find out the current usage of the appliance from its user manual.
2. Get the information on the supply voltage.
3. Multiply the values in steps 1 and 2 to get the power rating of your electrical appliance.
Purnima Singh, PhD
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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