What is the mathematical expression for Joule's law of heating effect?

Joule's law of heating effect describes the power dissipated as heat in an electrical conductor when an electric current flows through it. The mathematical expression, ( P = I^2R ), represents this relationship, where ( P ) is the power (in watts), ( I ) is the current (in amperes) flowing through the conductor, and ( R ) is the resistance (in ohms) of the conductor.

This equation indicates that the power loss due to heat is proportional to the square of the current and the resistance of the conductor. When a current passes through a resistive material, the energy is converted into heat, and this relationship highlights how increasing the current will significantly raise the power loss due to the ( I^2 ) term.

Other forms of the power equation, such as ( P = IV ) or ( P = V^2/R ), are useful in different contexts but do not specifically describe the heating effect as outlined by Joule's law. The equation ( P = IV ) expresses the relationship of power with current and voltage under general circumstances, while ( P = V^2/R ) applies when voltage across a resistor is known. However, these expressions do not capture