At a voltage of 220V, 14.4 kJ of energy was released in the lamp for 4 minutes.

At a voltage of 220V, 14.4 kJ of energy was released in the lamp for 4 minutes. Determine the resistance of the lamp filament

According to the Joule-Lenz law, the amount of heat released on the rheostat can be calculated by the formula:
Q = U ^ 2 * t / R, where Q = 14.4 kJ = 14.4 * 10 ^ 3 J, U is the voltage in the lamp (U = 220 V), t is the current flow time (t = 4 min = 4 * 60 s = 240 s), R is the resistance of the lamp filament (Ohm).
Let us express and calculate from the formula the resistance of the lamp filament:
R = U ^ 2 * t / Q = 220 ^ 2 * 240 / 14.4 * 10 ^ 3 = 806.7 ohms.
Check: Ohm = B ^ 2 * s / J = B ^ 2 * s / (W * s) = B ^ 2 / (B * A) = B / A = Ohm.
Answer: The resistance of the lamp filament is 806.7 ohms.