Power in resistive elements: which equation directly computes power dissipation when both the voltage drop (E) across the resistor and the current (I) through it are known?

Introduction / Context:
Power relationships in circuits are foundational. Engineers often select formulas based on which quantities are measured. When both current and voltage are known across a component, there is a direct expression to compute power dissipation without needing resistance.

Given Data / Assumptions:

• Element is resistive for purposes of average power.
• Voltage drop E (volts) and current I (amperes) are known.
• We seek instantaneous or average power in the simple V–I form.

Concept / Approach:
The fundamental power relation is P = V * I. For a resistor, this gives the real power converted to heat. Alternative forms P = I^2 * R and P = V^2 / R come from substituting Ohm’s law when only one of V or I is known along with R.

Step-by-Step Solution:

Verification / Alternative check:
Cross-check by Ohm’s law: If R is known, P = I^2 * R = V^2 / R = V * I; all are consistent when the correct substitutions are made.

Why Other Options Are Wrong:

Common Pitfalls:
Using a form requiring R when R is not known or mixing average power with reactive power in AC circuits.

Final Answer:
P = IE.