Heat produced: H = I²Rt
Joule's law of heating.
Twice the current
A current of 1 A flows through a resistor for a while and produces some heat. Then a current of 2 A flows through the same resistor for the same time.
How does the heat produced compare?
What this lesson covers
The idea
Moving charge Q through potential difference V takes energy VQ = VIt, dissipated in a resistor as heat: H = VIt = I²Rt (Joule's law of heating), so heat is proportional to the square of current, to resistance and time.
Twice the current
A current of 1 A flows through a resistor for a while and produces some heat. Then a current of 2 A flows through the same resistor for the same time.
How does the heat produced compare?
- It is 4 times as much
- It is 2 times as much
- It is the same
Heat in a resistor
Use the sliders. Watch how the heat H changes. One bar is 400 J.
A square
Doubling the current made the heat four times. Doubling the resistance or the time made it only two times. The current counts twice, because V = IR itself contains I.
Moving charge Q through a potential difference V takes energy VQ = VIt, which is dissipated in a resistor as heat: H = VIt = I²Rt. This is Joule's law of heating: the heat is proportional to the square of the current, to the resistance and to the time.
Notes
H = VIt = I²Rt (Joule's law of heating): the heat produced in a resistor is proportional to the square of the current, to the resistance and to the time.
Check yourself
A current of 2 A flows through a 5 Ω resistor for 10 s. How much heat is produced, in J?
Answer: 200 J
H = I²Rt = 2 × 2 × 5 × 10 = 200 J.
A potential difference of 6 V sends a current of 2 A through a resistor for 5 s. What heat is produced, in J?
Answer: 60 J
H = VIt = 6 V × 2 A × 5 s = 60 J.
The current through a resistor is doubled. The resistance and the time stay the same. What happens to the heat produced?
The resistance of a resistor is doubled. The current and the time stay the same. What happens to the heat produced?
- It becomes 4 times as much — correct. Yes!
- It becomes 2 times as much. Heat is proportional to the square of the current, so doubling the current gives 2 × 2 = 4 times the heat.
- It stays the same. H = I²Rt, so with the same R and t a different I gives a different H.
- It becomes 4 times as much. Heat is directly proportional to the resistance, not to its square, so doubling R doubles H.
- It becomes 2 times as much — correct. Yes!
- It becomes half. For a given current the heat is directly proportional to the resistance, so a larger R gives more heat.