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[ V_t = \varepsilon - Ir ]
Since energy ((E)) is power multiplied by time, the electrical work converted into heat over time (t) is (E = IVt).
[ P = IV ]
In the macroscopic world, we often observe that electrical devices—from a simple toaster to a supercomputer—become warm during operation. This phenomenon is not merely a nuisance or a byproduct of inefficiency; it is a fundamental manifestation of energy transfer governed by the principles of electromagnetism and thermodynamics. IB Physics Topic 5.2, "Heating Effect of Electric Currents," explores the precise relationship between electrical work and internal energy, introducing core concepts such as electrical power, resistance, Ohm’s law, and the distinction between direct current (DC) and alternating current (AC) in practical applications. The Origin of Heating: Resistance and Collisions At the heart of the heating effect is electrical resistance . When a potential difference (voltage) is applied across a conductor, it establishes an electric field that accelerates free electrons. However, these electrons do not move unimpeded; they continuously collide with the fixed, vibrating positive ions of the metallic lattice. Each collision transfers kinetic energy from the electron to the ion. Consequently, the amplitude of vibration of the ions increases, which is macroscopically observed as a rise in temperature—an increase in the internal energy of the material. Thus, resistance is the property that converts organized electrical work into disordered thermal energy. Power and Energy: The Fundamental Equations The rate at which this heating occurs is defined as electrical power ((P)). The IB syllabus emphasizes that for any component, the power dissipated (as heat or light) is the product of the voltage ((V)) across it and the current ((I)) through it:
Alternatively, substituting (I = V/R) gives:
The lost volts ((Ir)) are dissipated as heat inside the source. This explains why batteries become warm during heavy use and why a car battery’s voltage drops when starting the engine. The maximum power transfer theorem (often a HL extension) states that to extract maximum power from a source, the load resistance must equal the internal resistance, but this condition results in 50% efficiency—half the power is wasted as heat inside the source. The heating effect behaves differently under DC and AC. With DC, the current is constant, so the power dissipation is steady: (P = I^2R). With AC, the current varies sinusoidally. Since heating depends on (I^2), the average power is not zero (even though the average current over a cycle is zero). IB Physics introduces the root-mean-square (rms) values for AC:
[ P = \frac{V^2}{R} ]
[ I_{\text{rms}} = \frac{I_0}{\sqrt{2}}, \quad V_{\text{rms}} = \frac{V_0}{\sqrt{2}} ]
