Final answer:
The formula for heat produced as a function of current over a period of time is Q = I²R × t, with Q representing the heat produced, I the current, R the resistance, and t the time period.
Step-by-step explanation:
The formula for heat produced as a function of current over a period of time can be derived from the formula for electrical power, which is power (P) = voltage (V) × current (I). However, if there's a resistance in the circuit, the formula we use is P = I²R, where I is the current and R is the resistance. To find the heat (Q) produced over time (t), we integrate the power over that time, which leads to Q = P × t = I²R × t. This formula indicates that the heat produced in a resistor over time is directly proportional to the square of the current, the resistance, and the time for which the current flows.