Electric Power Dissipation Calculator

Calculate electric power using P=IV, P=I²R, or P=V²/R. Find heat dissipated in resistors.

3600s = 1 hour
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Power, Resistance, and Heat in Electric Circuits

Electrical power is the rate at which electrical energy is transferred or converted. The general DC relation P=IV says that a device receiving current I through a potential difference V converts energy at a rate measured in watts. For an ohmic resistor, combining this relation with V=IR gives P=I2R and P=V2/R. These three forms are equivalent only when the quantities refer to the same component and Ohm's law applies.

The squared terms reveal an important design lesson. If current is fixed, doubling resistance doubles dissipation because P=I2R. If voltage is fixed, doubling resistance halves dissipation because P=V2/R. There is no contradiction: changing resistance affects current differently depending on what the source holds constant.

P=IV=I2R=V2/R,   E=Pt
SymbolMeaningWhy it appears / units
PElectrical powerW=J/s; energy conversion rate.
VVoltage across the componentV=J/C; energy transferred per unit charge.
ICurrent through the componentA=C/s; charge flow rate.
RResistanceΩ; relates voltage and current for an ohmic resistor.
EEnergy dissipatedJ; equals power multiplied by elapsed time.

For resistor selection, calculated power is not the same as an acceptable power rating. Components need margin because resistance, ambient temperature, ventilation, enclosure conditions, and transient loads affect temperature rise. In AC circuits, the familiar power forms use RMS voltage and current for purely resistive loads; reactive or nonsinusoidal loads require the appropriate real-power treatment.

Worked Examples

Example 1: Resistor: I=2A, R=6Ω
P=I²R=4×6
Result: P=24W, V=12V
Heat dissipated in resistor
Example 2: Heater: V=230V, R=50Ω
P=230²/50=52900/50
Result: P=1058W ≈ 1kW
Standard electric heater
Example 3: Checking a resistor power rating
V=5.0V across R=220Ω → P=V2/R=25/220
Result: P≈0.114W
A 0.125W resistor would have very little margin; designers commonly choose a higher rating after considering operating conditions.
Example 4: Energy from a constant load
V=12V, I=0.50A, t=180s → P=6W and E=Pt
Result: E=1080J
Watts describe the rate of conversion; joules describe how much energy is converted over the full time interval.

Common Mistakes

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Confusing power with energy

Power is measured in watts and tells how fast energy is transferred. Energy is measured in joules or watt-hours and requires multiplying power by time.

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Using kΩ as though it were Ω

A value of 4.7kΩ is 4700Ω. Missing the factor of 1000 can change P=V2/R by three orders of magnitude.

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Using peak AC values in a formula intended for RMS values

For a purely resistive sinusoidal load, average real power is VrmsIrms. Peak voltage and peak current need the corresponding averaging relationship.

Frequently Asked Questions

Why three equivalent formulas?
P=IV, P=I²R, P=V²/R — all equivalent via Ohm's law V=IR. Choose based on what you know: Current limiter → use I²R (current is controlled). Voltage source → use V²/R (voltage is fixed).
Maximum power transfer vs efficiency?
At R_L=R_source: maximum power delivered to load, but efficiency=50% (half wasted). For maximum efficiency: R_L>>R_source. Communications (antennas): maximize power. Power systems (grid): maximize efficiency.
Why does a resistor get hot?
The electric field transfers energy to charge carriers, which interact with the material lattice and other microscopic degrees of freedom. Electrical energy is thereby converted mainly into thermal energy. The macroscopic rate of that conversion is the resistor's dissipated power.
Why can P=I2R and P=V2/R seem to predict opposite effects?
They describe different controlled conditions. With fixed current, increasing R raises power. With fixed voltage, increasing R reduces current strongly enough that power falls. Always identify which circuit quantity is actually held constant before interpreting a resistance change.
Does a 1 W resistor always dissipate 1 W?
No. A 1 W marking is a maximum rating under specified thermal conditions, not the amount the resistor automatically consumes. Actual dissipation is set by the voltage and current in the circuit. Good design normally keeps operating dissipation below the rating with appropriate margin.
Can the DC power formulas be used for AC?
For a purely resistive load, using RMS voltage and RMS current gives the correct average power. For loads with phase shift, real power is VrmsIrmscosφ. Nonsinusoidal waveforms may require waveform-based RMS and real-power calculations.

Formula Explorer connections

Interpretation: This formula links charge, voltage, current, resistance, capacitance, power or circuit time response. Assumption: Confirm DC versus AC conditions, RMS versus peak values, component topology and steady-state versus transient behavior. Ideal components may be assumed.

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