P = R * I²
Ep = R * I² * t
P = Dispersed power (W)
R = Resistance (Ω)
I = Current (A)
Ep = Dispersed energy (J)
t = Time (sec)
Calculate the heat energy dissipated in resistive elements of a circuit.
"Power dissipated in the form of heat in the resistive elements of the circuit."
Q = I² × R × t
or
Q = P × t
Where:
Q: Heat energy (joules, J)
I: Current (amperes, A)
R: Resistance (ohms, Ω)
t: Time (seconds, s)
P: Power (watts, W)
Note: Both formulas are equivalent. Use $ Q = I^2 R t $ when you know current and resistance.
The tendency of a material to oppose the flow of electric current, measured in ohms (Ω).
Higher resistance leads to more heat generation for the same current.
Example: A 100 Ω resistor limits current and produces heat.
Electrical power supplied or absorbed by a component, measured in watts (W).
1 watt = 1 joule per second.
You can calculate it as: P = I² × R or P = V × I
Example: A 5W LED uses 5 joules every second.
The flow of electric charge through a material, measured in amperes (A).
Heat is proportional to the square of the current — doubling current quadruples heat!
Example: 1 A, 2 A, 10 A — each produces vastly different heat levels.
Duration for which current flows, measured in seconds (s).
Longer time → more total heat generated.
Example: 1 second vs. 60 seconds → 60x more heat.
When current flows through a resistor:
Electrons move through the material
They collide with atoms, losing kinetic energy
This energy is transferred as vibrational energy → heat
Total heat depends on: current, resistance, and duration
The process is irreversible — electrical energy is lost as heat.
1. Designing heating elements (e.g., electric stoves, hair dryers)
2. Calculating power loss in transmission lines
3. Estimating temperature rise in PCB traces and components
4. Selecting appropriate resistors based on power rating
5. Understanding why devices get hot during operation
6. Safety analysis in circuits (preventing overheating and fire risk)
According to Joule's Law Q = I² × R × t, heat is proportional to the square of the current. When the current increases from 1A to 2A, the heat doesn't just double — it increases by 2² = 4 times; at 3A, it becomes 9 times.
This is why high-current circuits generate so much heat, and it's a key reason for selecting appropriate wire gauges and fuses.
The two formulas are essentially equivalent since P = I² × R. The difference lies in what you know: when you have current (I) and resistance (R), Q = I² × R × t is more convenient; when you know the power (P), Q = P × t is simpler.
For example, a 100W heater running for 1 hour can be calculated directly as Q = 100 × 3600 = 360,000 J, without needing to know the internal resistance or current.
By entering the current, resistance, and operating time in a circuit, you can calculate the total heat (in Joules) generated by resistive elements. If the calculated heat is too high, it indicates the component may overheat, posing a risk of damage or fire.
In practice, you can compare the result with the resistor's power rating to assess safety: for example, if a 0.25W-rated resistor actually dissipates 1W, it far exceeds its capacity, and a higher-power resistor or circuit redesign is required.
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