Power Dissipation Estimator

Physics Electricity and Magnetism • Current and Circuits

Written by STEM Calculators Team Published January 14, 2026 Updated February 24, 2026

6. Power Dissipation Estimator

Estimate electrical power dissipated as heat: $P = I^2R = \dfrac{V^2}{R} = IV$ . Includes a simple circuit total mode (series/parallel), AC average power preview, and a heat-glow animation hint.

Inputs support: pi, e, sqrt(), sin, cos, exp, log. Use * for multiplication.

Mode + Inputs

Mode: Single: given values: Resistance $R$ (Ω): Current $I$ (A): Voltage $V$ (V): Circuit: topology: Circuit: source voltage $V_s$ (V): Circuit: number of resistors: $R_1$ (Ω): $R_2$ (Ω): $R_3$ (Ω): $R_4$ (Ω): $R_5$ (Ω): $R_6$ (Ω): Circuit: “load” element for efficiency: AC: $V_{\mathrm{rms}}$ (V): AC: $I_{\mathrm{rms}}$ (A): AC: power factor $\cos\varphi$: Rating preset: Power rating $P_{\text{rated}}$ (W): Thermal resistance $\theta$ (°C/W): Ambient $T_{\text{amb}}$ (°C): Plot: Plot x-axis: Plot max x-value: Cursor fraction (dot) $f\in[0,1]$: Play speed:

Cursor fraction moves a dot along the plotted power curve from $x=0$ to $x=x_{\max}$. It does not change your input values.

Ready

Steps

Enter values and click Solve.

Heat glow + circuit sketch

Heat glow (based on $P/P_{\text{rated}}$)

Circuit sketch (single/circuit modes)

This is a qualitative visualization: real temperature rise depends on airflow, package, mounting, and material.

Power curve (pan/zoom)

Wheel to zoom • drag to pan • double-click resets

Hover: (x, P)=…

The curve uses the equivalent resistance $R_{\mathrm{eq}}$ for circuit mode. For resistive AC, average power uses RMS values.

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Power Dissipation (Joule Heating) — Theory

When current flows through a resistance, electrical energy is converted into heat (Joule heating). The instantaneous power dissipated in a resistor can be written in several equivalent forms.

1) Equivalent power formulas

\[ P = IV = I^2R = \frac{V^2}{R}. \]

These are equivalent as long as Ohm’s law $V=IR$ applies.

2) Circuit totals

For purely resistive series/parallel networks, you can reduce the circuit to an equivalent resistance $R_{\mathrm{eq}}$, then use the same power relations with the source voltage/current.

Series

\[ R_{\mathrm{eq}}=\sum_i R_i,\qquad I_{\text{tot}}=\frac{V_s}{R_{\mathrm{eq}}},\qquad P_{\text{tot}}=V_s I_{\text{tot}}. \]

Parallel

\[ \frac{1}{R_{\mathrm{eq}}}=\sum_i \frac{1}{R_i},\qquad I_{\text{tot}}=\frac{V_s}{R_{\mathrm{eq}}},\qquad P_{\text{tot}}=\sum_i \frac{V_s^2}{R_i}. \]

3) Heating and a simple temperature-rise hint

A common first-pass estimate treats the device as a lumped thermal system: $\Delta T \approx \theta P$, where $\theta$ is thermal resistance (°C/W).

\[ \Delta T \approx \theta P,\qquad T \approx T_{\text{amb}}+\Delta T. \]

This is approximate. Real temperature depends strongly on airflow, package size, mounting, and heat sinking.

4) AC average power (university preview)

For sinusoidal AC, the average (real) power is written using RMS values and power factor:

\[ P_{\text{avg}} = V_{\mathrm{rms}} I_{\mathrm{rms}} \cos\varphi. \]

For an ideal resistor, $\cos\varphi \approx 1$, so $P_{\text{avg}} \approx V_{\mathrm{rms}} I_{\mathrm{rms}}$.

5) Plot interaction note

The plot shows $P$ as a function of either current $I$ (using $P=I^2R_{\mathrm{eq}}$) or voltage $V$ (using $P=V^2/R_{\mathrm{eq}}$). The cursor slider only moves a dot along the plotted range; it does not alter your input values.