- Joule’s Law Definition: Joule’s Law of Heating is defined as the principle that the heat produced in a wire is proportional to the square of the current, the resistance of the wire, and the time the current flows.
- Formula of Joule’s Law: The formula H = I²Rt describes the heat produced, where H is heat in joules, I is current in amperes, R is resistance in ohms, and t is time in seconds.
- Current and Heat: The amount of heat generated is proportional to the square of the current flowing through the wire.
- Resistance Impact: The electrical resistance of the wire is directly proportional to the heat produced when current flows.
- Practical Applications: Joule’s Law of Heating explains heat generation in electrical systems, which is crucial for designing safe electrical appliances.
When current flows through a resistor, electrical energy is transferred to the material. Interactions between charge carriers and the material’s atoms convert that energy into thermal energy. The relationship between current, resistance and heating is called Joule’s law, after the physicist James Prescott Joule.
What is Joule’s Law of Heating
For a resistor carrying constant current I for time t, the electrical energy converted to heat is H = I²Rt joules. This form of Joule’s law assumes that I and R remain constant over the interval.
- With time and electrical resistance fixed, the heat is proportional to I². Doubling the current produces four times the heat under those conditions.
- With current and time fixed, the heat is proportional to the electrical resistance. This comparison does not apply when a fixed voltage, rather than fixed current, is the controlled condition.
- With current and electrical resistance fixed, the heat is proportional to elapsed time.
Combining the three proportionalities gives the following historical form. The conversion factor is needed only when heat is reported in calories rather than joules.
In SI units, H is energy in joules, I is current in amperes, R is resistance in ohms and t is time in seconds. The SI equation is H = I²Rt, with no J conversion factor. In the displayed legacy equation, J means Joule’s mechanical equivalent of heat in joules per calorie. The Mechanical equivalent of heat is a unit conversion, not an extra electrical property. NIST gives 1 thermochemical calorie as exactly 4.184 joules and 1 International Table calorie as exactly 4.1868 joules. The exact SI relationship is 1 erg = 10-7 joule. State the calorie or Btu definition when converting older heat units.
In SI form, Joule’s law gives H = I2Rt joules for a constant current of I amperes through a resistor of R ohms for t seconds. If current or resistance changes with time, calculate the energy from the integral of i²R with respect to time.
The preceding legacy image converts I²Rt to calories with the rounded factor 4.2. For an ohmic resistor with constant values, Ohm’s law also gives H = VIt = V²t/R = I²Rt in joules. Do not use V²t/R for a component whose resistance is not represented by V = IR over the interval.
Joule’s Law: Video Explanation
The video below provides another explanation of Joule’s law and its electrical-heating formulas.
For equipment design, use the component’s temperature-dependent resistance, thermal limits, duty cycle and heat-transfer conditions rather than relying on the constant-resistance equation alone.
