Ib Physics 5.2 <Reliable · 2027>

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 = IV ]

Alternatively, substituting (I = V/R) gives: Ib Physics 5.2

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

[ I_{\text{rms}} = \frac{I_0}{\sqrt{2}}, \quad V_{\text{rms}} = \frac{V_0}{\sqrt{2}} ] The lost volts ((Ir)) are dissipated as heat

[ P = I^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: The heating effect behaves differently under DC and AC

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: