Short Answer 
The equation P = IV defines the relationship between power (P), current (I), and voltage (V), showing that power in watts is the product of current in amperes and voltage in volts. The units are consistent, confirming the equation’s homogeneity, and it can be related to Ohm’s Law, yielding different formulations that reinforce its validity.
Step 1: Understand the Equation
The equation P = IV expresses the relationship between power (P), current (I), and voltage (V). This relationship indicates that power in watts is derived from multiplying current in amperes by voltage in volts. By noting that one watt equals one joule per second (J/s), we can confirm that this equation makes sense dimensionally.
Step 2: Analyze the Units
To check if the equation is homogenous, we examine the units involved. Each unit can be defined as follows:
- Power (P) is measured in watts (W).
- Electric current (I) is measured in amperes (A).
- Voltage (V) is measured in volts (V).
By substituting the definitions, we find that 1 watt is indeed equivalent to 1 joule per second, confirming the homogeneity of the equation.
Step 3: Relate to Ohm’s Law
Ohm’s law (V = IR) also underpins the relationship between voltage, current, and resistance. By substituting different forms of Ohm’s law into the equation for power, we can rewrite it as:
- P = V²/R (substituting I = V/R)
- P = I²R (substituting V = IR)
These variations consistently reflect the fundamental units of electric power, verifying that the initial equation P = IV is robust and homogenous across different representations.