Power in resistors: which equation directly computes power dissipation in a resistor when the voltage across it (E) and its resistance (R) are known?

Introduction / Context:
Resistor power dissipation can be computed using several equivalent formulas derived from Ohm’s law and the definition of power. Selecting the right form depends on which quantities are known. When voltage and resistance are given, a specific formula avoids intermediate steps and gives power directly.

Given Data / Assumptions:

• Known: voltage across the resistor E, resistance R.
• Ohm’s law applies: I = E / R.
• Power is defined as P = I * E for resistive elements.

Concept / Approach:
Start from P = I * E and substitute Ohm’s law (I = E / R) to eliminate current. This produces P = (E / R) * E = E^2 / R. Alternate forms P = I^2 * R or P = I * E are correct in general but require knowing I explicitly. The question asks for the formula that uses E and R directly.

Step-by-Step Solution:

Verification / Alternative check:
Example: E = 10 V, R = 5 ohm → P = E^2 / R = 100 / 5 = 20 W. Using P = I^2 * R with I = 10/5 = 2 A gives 2^2 * 5 = 20 W, confirming equivalence.

Why Other Options Are Wrong:

Common Pitfalls:
Using the wrong form for the known variables or mixing units (ensure volts and ohms yield watts). Always confirm by dimensional analysis: V^2 / ohm yields watts.

Final Answer:
P = E^2 / R