Ib Physics 5.2 Access

[ V_t = \varepsilon - Ir ]

[ P = \frac{V^2}{R} ]

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: Ib Physics 5.2

Alternatively, substituting (I = V/R) gives: [ V_t = \varepsilon - Ir ] [

These three equations are not interchangeable in all contexts. The form (P = I^2 R) is the most fundamental for heating because it explicitly shows that for a given current, heating increases linearly with resistance. Conversely, (P = V^2 / R) shows that for a fixed voltage (e.g., mains supply), a lower resistance produces more power—which explains why a short circuit (very low (R)) causes dangerously high power and fire. A critical refinement in Topic 5.2 is the concept of internal resistance ((r)). No real source of emf (electromotive force, (\varepsilon)), such as a battery or generator, is perfect. Internal resistance represents the inherent opposition to current flow within the source itself. When a current (I) flows, the terminal voltage (V_t) is less than the emf: Conversely, (P = V^2 / R) shows that for a fixed voltage (e

[ P = IV ]

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.