1. Definition and Physical Interpretation of Ohm's Law

Discovered by German physicist Georg Ohm, Ohm's Law is a fundamental law stating that the current flowing between two points in an electrical circuit is directly proportional to the voltage and inversely proportional to the resistance. It is the absolute foundational law for all electrical engineering decisions, including circuit design, safety analysis, and electrical installation diagnosis.

• Voltage (Voltage, V): The electrical pressure or potential difference that pushes electric charge (unit: Volt [V]), providing the energy for free electrons to move in a circuit.
• Current (Current, I): The flow of electric charge passing through a cross-section of a wire per unit time (unit: Ampere [A]). Physically, it corresponds to the drift velocity and density of free electrons.
• Resistance (Resistance, R): The property of a material that opposes the flow of electric current (unit: Ohm [Ω]), proportional to the frequency of collisions between free electrons and atoms in the conductor.

2. Deriving Ohm's Law and Power Calculation Formulas

The fundamental relationships for quantitatively calculating the state of an electrical circuit are as follows:

① Basic Ohm's Law Formula: The correlation formula between voltage (V), current (I), and resistance (R).

V = I × R  [V]

Using this, we can solve for current and resistance to obtain the following derived equations:

I = V / R  [A]    |    R = V / I  [Ω]

② Electric Power (P): The rate at which electrical energy is converted into other forms of energy, such as heat or light, as it passes through a resistor (unit: Watt [W]).

P = V × I  [W]

By combining Ohm's Law, the power calculation formula can be expanded as follows, allowing you to predict heat loss even if you only know the current flowing through the wire or the resistance value:

P = I^2 × R = V^2 / R  [W]

3. Wire Resistance Factors and Electrical Design Significance

In actual electrical design, not only simple resistors but also the inherent resistance of the wire itself is subject to Ohm's Law. The resistance of a wire is proportional to the resistivity of the material (ρ) and the length of the wire (L), and inversely proportional to the cross-sectional area (A).

R = ρ × (L / A)  [Ω]

If a wire is thin and long, its resistance increases sharply, leading to a voltage drop and wire heating (Joule heating) when current flows. When designing electrical installations, the cable cross-sectional area must be strictly selected based on allowable current capacity and Ohm's Law to prevent fires or equipment malfunctions.