Louis La Minh Hoang

In my physics revision lesson, we focused on electric power in circuits, but with a strong emphasis on optimization — finding when the power on a resistor is maximum or minimum using inequalities and algebraic reasoning, not just formulas.

We began by revisiting the definition of electric power, understanding it as the rate at which electrical energy is converted. From there, instead of treating power as a standalone formula, we connected it deeply with Ohm’s Law and circuit constraints such as fixed voltage or fixed total resistance. This was important because the behavior of power completely changes depending on what is held constant in the system.

The most interesting part was analyzing how power varies with resistance. By expressing power as a function of resistance, we transformed the problem into a mathematical inequality problem. Using techniques like completing the square or applying well-known inequality results, we could determine the exact conditions under which a power reaches a maximum value. This approach made it clear that the result isn’t magic — it’s a consequence of how current and resistance interact.

We also explored why, in some setups, increasing resistance increases power, while in others it decreases it. This required careful reasoning about current redistribution and energy dissipation, rather than blind substitution into formulas. The minimum power cases were just as important, helping us understand limiting behavior and extreme scenarios in circuits.

What made this lesson challenging wasn’t the formulas themselves, but the logical structure of the problems. Each question required setting up the correct expression, identifying constraints, and applying inequalities cleanly and rigorously. One small algebraic mistake could completely change the conclusion.

Overall, this revision showed me that electric power problems are a perfect blend of physics intuition and mathematical optimization. When inequalities are used properly, they turn complicated circuit behavior into something precise, elegant, and surprisingly satisfying to solve.