Joule's law states that the heat produced by an electric current passing through a conductor is directly proportional to the square of the current, the resistance of the conductor, and the time the current flows. This relationship can be expressed mathematically as Q = I^2 R t , where Q is the heat generated, I is the current, R is the resistance, and t is the time. This principle is important in electrical engineering and physics, as it helps in understanding how electrical energy is converted into heat. It also plays a crucial role in designing electrical systems to prevent overheating and ensure safety.