Yes, when an electric current flows through a wire, it generates heat due to the wire's resistance. This phenomenon is described by Joule's Law, which states that the heat (H) produced in a conductor is directly proportional to the square of the current (I), the resistance (R) of the wire, and the duration of time (t) during which the current flows. Mathematically, it can be represented as:
H = I^2 * R * t
This equation indicates that the amount of heat generated is proportional to the square of the current. So, if you double the current, the heat generated will increase by a factor of four. Similarly, the resistance of the wire also plays a significant role in determining the amount of heat generated. If the wire has higher resistance, more heat will be produced.
To determine the exact amount of heat generated, you would need to know the values of the current, resistance, and the time for which the current flows. The heat generated is usually measured in units of Joules (J) or calories (cal).