When the component obeys ((V = IR)), where (R) is constant resistance, we can derive two additional, situationally useful forms. Substituting (V = IR) into (P = IV) yields:

[ P = I^2 R ]

[ P = IV ]

[ I_{\text{rms}} = \frac{I_0}{\sqrt{2}}, \quad V_{\text{rms}} = \frac{V_0}{\sqrt{2}} ]

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:

These are defined such that an AC circuit dissipates the same average power in a resistor as a DC circuit with (I_{\text{rms}}) and (V_{\text{rms}}). Thus, (P_{\text{avg}} = I_{\text{rms}}^2 R = V_{\text{rms}} I_{\text{rms}}). This concept is essential for understanding household electricity: a 230 V AC mains supply means (V_{\text{rms}} = 230) V, with a peak voltage of about 325 V. The heating effect is harnessed in resistive devices like kettles, ovens, and incandescent bulbs (which operate at high temperatures, emitting visible light as a byproduct of heat). However, it also poses challenges. In long-distance power transmission, heating losses ((P_{\text{loss}} = I^2R)) are minimized by stepping up voltage (thereby reducing current) using transformers—a concept linking Topic 5.2 with Topic 5.4 (Magnetic Effects). Furthermore, circuit breakers and fuses rely on the heating effect: excessive current melts a fuse wire or triggers a bimetallic strip, breaking the circuit and preventing fire. Conclusion Topic 5.2 reveals that the heating effect of electric currents is not a mere accident but a predictable consequence of the conversion of electrical potential energy into internal thermal energy via collisions in a resistive medium. By mastering the relationships (P = IV), (P = I^2R), and (P = V^2/R), along with the real-world complication of internal resistance and the statistical equivalence of AC and DC via rms values, students gain a powerful toolkit. This knowledge not only explains why devices warm up but also underpins the design of efficient power systems and safe electrical installations—demonstrating how a microscopic collision of an electron with an atom scales up to light a city or charge a phone.

[ V_t = \varepsilon - Ir ]

Since energy ((E)) is power multiplied by time, the electrical work converted into heat over time (t) is (E = IVt).