☰ Contents · Physics

Joule–Lenz law and efficiency

Lessons 34–35 · 2 lessons · P.Q. Habibullayev, A. Boydedayev, A.D. Bahromov, J.E. Usarov, K.T. Suyarov, M.K. Yuldasheva. Physics, textbook for Grade 8 of general secondary schools, revised and enlarged 3rd edition. “O‘qituvchi” Publishing and Printing Creative House, Tashkent, 2019
34

Heating of conductors by electric current

Textbook: pp. 97–99
GoalKnow the Joule–Lenz law Q = I²Rt and use it to calculate the heating effect of current.
New words
Joule–Lenz law · Joul–Lens qonuniamount of heat · issiqlik miqdoriheating effect of current · tokning issiqlik ta’siriheating coil · qizdirgich spirali
Explanation

When current flows a conductor heats up, because the moving charges pass part of their energy to the substance of the conductor. According to the law found independently by the English physicist Joule and the Russian physicist Lenz, the heat released in a conductor is directly proportional to the square of the current, to the resistance and to the time: Q = I²Rt. If all the work of the current turns into heat, Q = A, so Q = IUt = U²t/R is also correct. Heat is measured in joules. In series the current is the same, so more heat is released in the conductor of larger resistance; in parallel (same voltage) more is released in the conductor of smaller resistance. That is why connecting wires stay cool while a heating coil gets red hot. Heaters can cause fires: do not use them without adult supervision.

Worked examples
R = 10 Ω, I = 3 A, t = 20 s: Q = I²Rt = 9 · 10 · 20 = 1800 J.
A coil at U = 24 V with R = 6 Ω, t = 1 min = 60 s: Q = U²t/R = 576 · 60 : 6 = 5760 J.
Class activity

In your notebook make a table: for two conductors in series (R₁ = 2 Ω, R₂ = 8 Ω, I = 1 A, t = 10 s) calculate Q₁ and Q₂ and conclude which heats more. Do not connect anything to a current.

Practice
1
State the Joule–Lenz law and write its formula.
2
R = 5 Ω, I = 4 A, t = 30 s. Q in J?
3
U = 12 V, R = 4 Ω, t = 10 s. Q = U²t/R in J?
4
Why does a lamp filament heat much more than the connecting wires, although the current is the same?