# Power Dissipation Calculator for Series and Parallel Circuits

## This tool will calculate the power dissipation of series or parallel resistor circuits given the input voltage and the resistance values.

Inputs

Connection Type:

Voltage:

R - {{ key + 1}}
X

Outputs

P - {{ key + 1}}

### Calculator Operation

- Select either series or parallel for the type of resistive circuit
- Enter the source voltage
- Enter a resistance value for at least one resistor
- Add additional resistors by pushing the "+ Add resistor" button
- Remove resistors by pushing the "x" button to the left of the value box
- Push the calculate button to determine the power dissipated by each resistor

### Series Circuit Schematic and Power Equations

Figure 1 is the circuit schematic for resistors connected in series with an applied voltage V.

*Figure 1. Resistive series circuit schematic for power dissipation calculation*

For a series circuit, the total resistance is the sum of the individual resistors:

$$R_{total} = R_1 + R_2 + \dots + R_n$$

The current through each resistor is then given by:

$$I = \frac{V}{R_{total}}$$

Finally, the power dissipated by each resistor is calculated as

$$P_n = I^2R_n$$

### Parallel Circuit Schematic and Power Equations

The parallel resistor circuit is shown in Figure 2.

*Figure 2. Resistive parallel circuit schematic for power dissipation calculation*

For the parallel circuit of Figure 2, the voltage is the same across all of the resistors. Therefore, we can calculate the power dissipation of each individual resistor by:

$$P_n = \frac{V^2}{R_n}$$

### Further Reading

- Textbook: Series Circuits and the Applications of Ohm's Law
- Textbook: Parallel Circuits and the Applications of Ohm's Law
- Forum: Power Dissipation Calculations

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